 Look up thousand or 1000 in Wiktionary, the free dictionary. 1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000. It may also be described as the short thousand in historical discussion of medieval contexts where it might be confused with the Germanic concept of the "long thousand" (1200). A period of 1,000 years is sometimes termed, after the Greek root, a chiliad. A chiliad of other objects means 1,000 of them.[1] Notation[edit]
Properties[edit]There are 168 prime numbers less than 1000. 1000 is the 10th icositetragonal number, or 24-gonal number.[2] 1000 has a reduced totient value of 100, and totient of 400. It is equal to the sum of Euler's totient function over the first 57 integers, with 11 integers having a totient value of 1000. 1000 is the smallest number that generates three primes in the fastest way possible by concatenation of decremented numbers: (1,000,999), (1,000,999,998,997), and (1,000,999,998,997,996,995,994,993) are all prime.[3] Selected numbers in the range 1001–1999[edit]1001 to 1099[edit]1001 = sphenic number (7 × 11 × 13), pentagonal number, pentatope number1002 = sphenic number, Mertens function zero, abundant number, number of partitions of 221003 = the product of some prime p and the pth prime, namely p = 17.1004 = heptanacci number[4]1005 = Mertens function zero, decagonal pyramidal number[5]1006 = number that is the sum of 7 positive 5th powers[6]1007 = number that is the sum of 8 positive 5th powers[7]1008 = divisible by the number of primes below it1009 = smallest four-digit prime, palindromic in bases 11, 15, 19, 24 and 28: (83811, 47415, 2F219, 1I124, 18128). It is also a Lucky prime and Chen prime.1010 = 103 + 10,[8] Mertens function zero1011 = the largest n such that 2n contains 101 and doesn't contain 11011, Harshad number in bases 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75 (and 202 other bases), number of partitions of 1 into reciprocals of positive integers <= 16 Egyptian fraction[9]1012 = ternary number, (3210) quadruple triangular number (triangular number is 253),[10] number of partitions of 1 into reciprocals of positive integers <= 17 Egyptian fraction[9]1013 = Sophie Germain prime,[11] centered square number,[12] Mertens function zero1014 = 210-10,[13] Mertens function zero, sum of the nontriangular numbers between successive triangular numbers1015 = square pyramidal number[14]1016 = member of the Mian–Chowla sequence,[15] stella octangula number, number of surface points on a cube with edge-length 14[16]1017 = generalized triacontagonal number[17]1018 = Mertens function zero, 101816 + 1 is prime[18]1019 = Sophie Germain prime,[11] safe prime,[19] Chen prime1020 = polydivisible number1021 = twin prime with 1019. It is also a Lucky prime.1022 = Friedman number1023 = sum of five consecutive primes (193 + 197 + 199 + 211 + 223);[20] the number of three-dimensional polycubes with 7 cells;[21] number of elements in a 9-simplex; highest number one can count to on one's fingers using binary; magic number used in Global Positioning System signals.1024 = 322 = 45 = 210, the number of bytes in a kilobyte (in 1999, the IEC coined kibibyte to use for 1024 with kilobyte being 1000, but this convention has not been widely adopted). 1024 is the smallest 4-digit square and also a Friedman number.1025 = Proth number 210 + 1; member of Moser–de Bruijn sequence, because its base-4 representation (1000014) contains only digits 0 and 1, or it's a sum of distinct powers of 4 (45 + 40); Jacobsthal-Lucas number; hypotenuse of primitive Pythagorean triangle1026 = sum of two distinct powers of 2 (1024 + 2)1027 = sum of the squares of the first eight primes; can be written from base 2 to base 18 using only the digits 0 to 9.1028 = sum of totient function for first 58 integers; can be written from base 2 to base 18 using only the digits 0 to 9; number of primes <= 213.[22]1029 = can be written from base 2 to base 18 using only the digits 0 to 9.1030 = generalized heptagonal number1031 = exponent and number of ones for the largest proven base-10 repunit prime,[23] Sophie Germain prime,[11] super-prime, Chen prime1032 = sum of two distinct powers of 2 (1024 + 8)1033 = emirp, twin prime with 10311034 = sum of 12 positive 9th powers[24]1035 = triangular number,[25] hexagonal number[26]1036 = central polygonal number[27]1037 = number in E-toothpick sequence[28]1038 = even integer that is an unordered sum of two primes in exactly n ways[29]1039 = prime of the form 8n+7,[30] number of partitions of 30 that do not contain 1 as a part,[31] Chen prime1040 = 45 + 42: sum of distinct powers of 4[32]1041 = sum of 11 positive 5th powers[33]1042 = sum of 12 positive 5th powers[34]1043 = number whose sum of even digits and sum of odd digits are even[35]1044 = sum of distinct powers of 4[32]1045 = octagonal number[36]1046 = coefficient of f(q) (3rd order mock theta function)[37]1047 = number of ways to split a strict composition of n into contiguous subsequences that have the same sum[38]1048 = number of partitions of n into squarefree parts[39]1049 = Sophie Germain prime,[11] highly cototient number,[40] Chen prime1050 = 10508 to decimal becomes a pronic number (55210),[41] number of parts in all partitions of 29 into distinct parts[42]1051 = centered pentagonal number,[43] centered decagonal number1052 = number that is the sum of 9 positive 6th powers[44]1053 = triangular matchstick number[45]1054 = centered triangular number[46]1055 = number that is the sum of 12 positive 6th powers[47]1056 = pronic number[48]1057 = central polygonal number[49]1058 = number that is the sum of 4 positive 5th powers,[50] area of a square with diagonal 46[51]1059 = number n such that n4 is written in the form of a sum of four positive 4th powers[52]1060 = sum of the first 25 primes1061 = emirp, twin prime with 10631062 = number that is not the sum of two palindromes[53]1063 = super-prime, sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167); near-wall-sun-sun prime[54]1064 = sum of two positive cubes[55]1065 = generalized duodecagonal[56]1066 = number whose sum of their divisors is a square[57]1067 = number of strict integer partitions of n in which are empty or have smallest part not dividing the other ones[58]1068 = number that is the sum of 7 positive 5th powers,[6] total number of parts in all partitions of 15[59]1069 = emirp[60]1070 = number that is the sum of 9 positive 5th powers[61]1071 = heptagonal number[62]1072 = centered heptagonal number[63]1073 = number that is the sum of 12 positive 5th powers[34]1074 = number that is not the sum of two palindromes[53]1075 = number non-sum of two palindromes[53]1076 = number of strict trees weight n[64]1077 = number where 7 outnumbers every other digit in the number[65]1078 = Euler transform of negative integers[66]1079 = every positive integer is the sum of at most 1079 tenth powers.1080 = pentagonal number[67]1081 = triangular number,[25] member of Padovan sequence[68]1082 = central polygonal number[27]1083 = three-quarter square,[69] number of partitions of 53 into prime parts1084 = third spoke of a hexagonal spiral,[70] 108464 + 1 is prime1085 = number of partitions of n into distinct parts > or = 2[71]1086 = Smith number,[72] sum of totient function for first 59 integers1087 = super-prime, cousin prime, lucky prime[73]1088 = octo-triangular number, (triangular number result being 136)[74] sum of two distinct powers of 2, (1024 + 64)[75] number that is divisible by exactly seven primes with the inclusion of multiplicity[76]1089 = 332, nonagonal number, centered octagonal number, first natural number whose digits in its decimal representation get reversed when multiplied by 9.[77]1090 = sum of 5 positive 5th powers[78]1091 = cousin prime and twin prime with 10931092 = divisible by the number of primes below it1093 = the smallest Wieferich prime (the only other known Wieferich prime is 3511[79]), twin prime with 1091 and star number[80]1094 = sum of 9 positive 5th powers,[61] 109464 + 1 is prime1095 = sum of 10 positive 5th powers,[81] number that is not the sum of two palindromes1096 = hendecagonal number,[82] number of strict solid partitions of 18[83]1097 = emirp,[60] Chen prime1098 = multiple of 9 containing digit 9 in its base-10 representation[84]1099 = number where 9 outnumbers every other digit[85]1100 to 1199[edit]1100 = number of partitions of 61 into distinct squarefree parts[86]1101 = pinwheel number[87]1102 = sum of totient function for first 60 integers1103 = Sophie Germain prime,[11] balanced prime[88]1104 = Keith number[89]1105 = 332 + 42 = 322 + 92 = 312 + 122 = 232 + 242, Carmichael number,[90] magic constant of n × n normal magic square and n-queens problem for n = 13, decagonal number,[91] centered square number,[12] Fermat pseudoprime[92]1106 = number of regions into which the plane is divided when drawing 24 ellipses[93]1107 = number of non-isomorphic strict T0 multiset partitions of weight 8[94]1108 = number k such that k64 + 1 is prime1109 = Friedlander-Iwaniec prime,[95] Chen prime1110 = k such that 2k + 3 is prime[96]1111 = repdigit1112 = k such that 9k - 2 is a prime[97]1113 = number of strict partions of 40[98]1114 = number of ways to write 22 as an orderless product of orderless sums[99]1115 = number of partitions of 27 into a prime number of parts[100]1116 = divisible by the number of primes below it1117 = number of diagonally symmetric polyominoes with 16 cells,[101] Chen prime1118 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,21}[102]1119 = number of bipartite graphs with 9 nodes[103]1120 = number k such that k64 + 1 is prime1121 = number of squares between 342 and 344.[104]1122 = pronic number,[48] divisible by the number of primes below it1123 = balanced prime[88]1124 = Leyland number[105]1125 = Achilles number1126 = number of 2 × 2 non-singular integer matrices with entries from {0, 1, 2, 3, 4, 5}[106]1127 = maximal number of pieces that can be obtained by cutting an annulus with 46 cuts[107]1128 = triangular number,[25] hexagonal number,[26] divisible by the number of primes below it1129 = number of lattice points inside a circle of radius 19[108]1130 = skiponacci number[109]1131 = number of edges in the hexagonal triangle T(26)[110]1134 = divisible by the number of primes below it, triangular matchstick number[45] 1135 = centered triangular number[111]1136 = number of independent vertex sets and vertex covers in the 7-sunlet graph[112]1137 = sum of values of vertices at level 5 of the hyperbolic Pascal pyramid[113]1138 = recurring number in the works of George Lucas and his companies, beginning with his first feature film – THX 1138; particularly, a special code for Easter eggs on Star Wars DVDs.1139 = wiener index of the windmill graph D(3,17)[114]1140 = tetrahedral number[115]1141 = 7-Knödel number[116]1142 = n such that n32 + 1 is prime[117]1145 = 5-Knödel number[118]1151 = first prime following a prime gap of 22.[119], Chen prime1152 = highly totient number,[120] 3-smooth number (27×32), area of a square with diagonal 48,[51] Achilles number1153 = super-prime, Proth prime[121]1154 = 2 × 242 + 2 = number of points on surface of tetrahedron with edgelength 24[122]1155 = number of edges in the join of two cycle graphs, both of order 33[123]1156 = 342, octahedral number,[124] centered pentagonal number,[43] centered hendecagonal number.[125] 1158 = number of points on surface of octahedron with edgelength 17[126]1159 = member of the Mian–Chowla sequence,[15] a centered octahedral number[127]1160 = octagonal number[128]1161 = sum of the first 26 primes1162 = pentagonal number,[67] sum of totient function for first 61 integers1163 = smallest prime > 342.[129] See Legendre's conjecture. Chen prime.1165 = 5-Knödel number[130]1166 = heptagonal pyramidal number[131]1167 = number of rational numbers which can be constructed from the set of integers between 1 and 43[132]1169 = highly cototient number[40]1170 = highest possible score in a National Academic Quiz Tournaments (NAQT) match1171 = super-prime1174 = number of widely totally strongly normal compositions of 161175 = maximal number of pieces that can be obtained by cutting an annulus with 47 cuts[133]1176 = triangular number[25]1177 = heptagonal number[62]1178 = number of surface points on a cube with edge-length 15[16]1183 = pentagonal pyramidal number1184 = amicable number with 1210[134]1185 = number of partitions of 45 into pairwise relatively prime parts[135]1186 = number of diagonally symmetric polyominoes with 15 cells,[136] number of partitions of 54 into prime parts1187 = safe prime,[19] Stern prime,[137] balanced prime,[88] Chen prime1189 = number of squares between 352 and 354.[138]1190 = pronic number,[48] number of cards to build an 28-tier house of cards[139] 1191 = 352 - 35 + 1 = H35 (the 35th Hogben number)[140]1192 = sum of totient function for first 62 integers1193 = a number such that 41193 - 31193 is prime, Chen prime1196 = [141]1197 = pinwheel number[87]1198 = centered heptagonal number[63]1199 = area of the 20th conjoined trapezoid[142]1200 to 1299[edit]1200 = the long thousand, ten "long hundreds" of 120 each, the traditional reckoning of large numbers in Germanic languages, the number of households the Nielsen ratings sample,[143] number k such that k64 + 1 is prime1201 = centered square number,[12] super-prime, centered decagonal number1202 = number of regions the plane is divided into by 25 ellipses[144]1205 = number of partitions of 28 such that the number of odd parts is a part[145] 1207 = composite de Polignac number[146]1210 = amicable number with 1184[147]1211 = composite de Polignac number[148]1213 = emirp1214 = sum of first 39 composite numbers[149]1215 = number of edges in the hexagonal triangle T(27)[150]1216 = nonagonal number[151]1217 = super-prime, Proth prime[121]1218 = triangular matchstick number[45]1219 = Mertens function zero, centered triangular number[152]1220 = Mertens function zero, number of binary vectors of length 16 containing no singletons[153]1222 = hexagonal pyramidal number1223 = Sophie Germain prime,[11] balanced prime, 200th prime number[88]1224 = number of edges in the join of two cycle graphs, both of order 34[154]1225 = 352, square triangular number,[155] hexagonal number,[26] centered octagonal number[156]1228 = sum of totient function for first 63 integers1229 = Sophie Germain prime,[11] number of primes between 0 and 100001230 = the Mahonian number: T(9, 6)[157]1233 = 122 + 3321234 = number of parts in all partitions of 30 into distinct parts[158]1236 = 617 + 619: sum of twin prime pair[159]1237 = prime of the form 2p-11238 = number of partitions of 31 that do not contain 1 as a part[31]1240 = square pyramidal number[14]1241 = centered cube number[160]1242 = decagonal number[91]1243 = composite de Polignac number[161]1244 = number of complete partitions of 25[162]1247 = pentagonal number[67]1249 = emirp, trimorphic number[163]1250 = area of a square with diagonal 50[51]1251 = 2 × 252 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 25[164]1252 = 2 × 252 + 2 = number of points on surface of tetrahedron with edgelength 25[165]1253 = number of partitions of 23 with at least one distinct part[166]1255 = Mertens function zero, number of ways to write 23 as an orderless product of orderless sums,[167] number of partitions of 23[168]1256 = Mertens function zero1257 = number of lattice points inside a circle of radius 20[169]1258 = Mertens function zero1259 = highly cototient number[40]1260 = highly composite number,[170] pronic number,[48] the smallest vampire number,[171] sum of totient function for first 64 integers, number of strict partions of 41[172] and appears twice in the Book of Revelation1261 = star number,[80] Mertens function zero1262 = maximal number of regions the plane is divided into by drawing 36 circles[173]1263 = rounded total surface area of a regular tetrahedron with edge length 27[174]1264 = sum of the first 27 primes1265 = number of rooted trees with 43 vertices in which vertices at the same level have the same degree[175]1266 = centered pentagonal number,[43] Mertens function zero1267 = 7-Knödel number[176]1268 = number of partitions of 37 into prime power parts[177]1270 = Mertens function zero1271 = sum of first 40 composite numbers[178]1274 = sum of the nontriangular numbers between successive triangular numbers1275 = triangular number,[25] sum of the first 50 natural numbers1276 = number of irredundant sets in the 25-cocktail party graph[179]1278 = number of Narayana's cows and calves after 20 years[180]1279 = Mertens function zero, Mersenne prime exponent1280 = Mertens function zero, number of parts in all compositions of 9[181]1281 = octagonal number[182]1282 = Mertens function zero, number of partitions of 46 into pairwise relatively prime parts[183]1283 = safe prime[19]1284 = 641 + 643: sum of twin prime pair[184]1285 = Mertens function zero, number of free nonominoes, number of parallelogram polyominoes with 10 cells.[185]1288 = heptagonal number[62]1289 = Sophie Germain prime,[11] Mertens function zero1291 = Mertens function zero1292 = Mertens function zero1294 = rounded volume of a regular octahedron with edge length 14[186]1295 = number of edges in the join of two cycle graphs, both of order 35[187]1296 = 362 = 64, sum of the cubes of the first eight positive integers, the number of rectangles on a normal 8 × 8 chessboard, also the maximum font size allowed in Adobe InDesign1297 = super-prime, Mertens function zero, pinwheel number[87]1298 = number of partitions of 55 into prime parts1299 = Mertens function zero, number of partitions of 52 such that the smallest part is greater than or equal to number of parts[188]1300 to 1399[edit]1300 = Sum of the first 4 fifth powers, mertens function zero, largest possible win margin in an NAQT match1301 = centered square number,[12] Honaker prime[189]1302 = Mertens function zero, number of edges in the hexagonal triangle T(28)[190]1305 = triangular matchstick number[45]1306 = Mertens function zero. In base 10, raising the digits of 1306 to powers of successive integers equals itself: 1306 = 11 + 32 + 03 + 64. 135, 175, 518, and 598 also have this property. Centered triangular number.[191] 1307 = safe prime[19]1308 = sum of totient function for first 65 integers1309 = the first sphenic number followed by two consecutive such number1311 = number of integer partitions of 32 with no part dividing all the others[192]1312 = member of the Mian-Chowla sequence;[15] code for "ACAB" itself an acronym for "all cops are bastards"[193]1314 = number of integer partitions of 41 whose distinct parts are connected[194]1318 = Mertens function zero1319 = safe prime[19]1320 = 659 + 661: sum of twin prime pair[195]1321 = Friedlander-Iwaniec prime[196] 1322 = area of the 21th conjoined trapezoid[197]1323 = Achilles number1325 = Markov number,[198] centered tetrahedral number[199]1326 = triangular number,[25] hexagonal number,[26] Mertens function zero1327 = first prime followed by 33 consecutive composite numbers1328 = sum of totient function for first 66 integers1329 = Mertens function zero, sum of first 41 composite numbers[200]1330 = tetrahedral number,[105] forms a Ruth–Aaron pair with 1331 under second definition1331 = 113, centered heptagonal number,[63] forms a Ruth–Aaron pair with 1330 under second definition. This is the only non-trivial cube of the form x2 + x − 1, for x = 36.1332 = pronic number[48]1333 = 372 - 37 + 1 = H37 (the 37th Hogben number)[201]1334 = maximal number of regions the plane is divided into by drawing 37 circles[202]1335 = pentagonal number,[67] Mertens function zero1336 = Mertens function zero1337 = Used in the novel form of spelling called leet. Approximate melting point of gold in kelvins.1338 = Mertens function zero1340 = k such that 5 × 2k - 1 is prime[203]1342 = ,[204] Mertens function zero1343 = cropped hexagone[205]1344 = 372 - 52, the only way to express 1344 as a difference of prime squares[206]1345 = k such that k, k+1 and k+2 are products of two primes[207]1349 = Stern-Jacobsthal number[208]1350 = nonagonal number[151]1351 = number of partitions of 28 into a prime number of parts[209]1352 = number of surface points on a cube with edge-length 16,[16] Achilles number1353 = 2 × 262 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 26[210] 1354 = 2 × 262 + 2 = number of points on surface of tetrahedron with edgelength 26[211]1357 = number of nonnegative solutions to x2 + y2 ≤ 412[212]1358 = rounded total surface area of a regular tetrahedron with edge length 28[213]1360 = 372 - 32, the only way to express 1360 as a difference of prime squares[214]1361 = first prime following a prime gap of 34,[119] centered decagonal number, Honaker prime[215]1362 = number of achiral integer partitions of 48[216]1365 = pentatope number[217]1367 = safe prime,[19] balanced prime, sum of three, nine, and eleven consecutive primes (449 + 457 + 461, 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173, and 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151),[88]1368 = number of edges in the join of two cycle graphs, both of order 36[218]1369 = 372, centered octagonal number[156]1370 = σ2(37): sum of squares of divisors of 37[219]1371 = sum of the first 28 primes1372 = Achilles number1373 = number of lattice points inside a circle of radius 21[220]1374 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,23}[221]1375 = decagonal pyramidal number[222]1376 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)[223]1377 = maximal number of pieces that can be obtained by cutting an annulus with 51 cuts[224]1378 = triangular number[25]1379 = magic constant of n × n normal magic square and n-queens problem for n = 14.1380 = number of 8-step mappings with 4 inputs[225]1381 = centered pentagonal number[43]Mertens function zero1384 = [226]1385 = up/down number[227]1386 = octagonal pyramidal number[228]1387 = 5th Fermat pseudoprime of base 2,[229] 22nd centered hexagonal number and the 19th decagonal number,[91] second Super-Poulet number.[230]1389 = sum of first 42 composite numbers[231]1391 = number of rational numbers which can be constructed from the set of integers between 1 and 47[232]1392 = number of edges in the hexagonal triangle T(29)[233]1393 = 7-Knödel number[234]1394 = sum of totient function for first 67 integers1395 = vampire number,[171] member of the Mian–Chowla sequence[15] triangular matchstick number[45]1396 = centered triangular number[235]1398 = number of integer partitions of 40 whose distinct parts are connected[236]1400 to 1499[edit]1400 = number of sum-free subsets of {1, ..., 15}[237]1401 = pinwheel number[87]1402 = number of integer partitions of 48 whose augmented differences are distinct[238]1404 = heptagonal number[62]1405 = 262 + 272, 72 + 82 + ... + 162, centered square number[12]1406 = pronic number,[48] semi-meandric number[239]1407 = 382 - 38 + 1 = H38 (the 38th Hogben number)[240]1408 = maximal number of regions the plane is divided into by drawing 38 circles[241]1409 = super-prime, Sophie Germain prime,[11] smallest number whose eighth power is the sum of 8 eighth powers, Proth prime[121]1414 = smallest composite that when added to sum of prime factors reaches a prime after 27 iterations[242]1415 = the Mahonian number: T(8, 8)[157]1417 = number of partitions of 32 in which the number of parts divides 32[243]1419 = Zeisel number[244]1420 = Number of partitions of 56 into prime parts1423 = 200 + 1223 and the 200th prime is 1223[245]1424 = number of nonnegative solutions to x2 + y2 ≤ 422[246]1425 = self-descriptive number in base 51426 = sum of totient function for first 68 integers, pentagonal number,[67] number of strict partions of 42[247]1429 = number of partitions of 53 such that the smallest part is greater than or equal to number of parts[248]1430 = Catalan number[249]1431 = triangular number,[25] hexagonal number[26]1432 = member of Padovan sequence[68]1433 = super-prime, Honaker prime,[250] typical port used for remote connections to Microsoft SQL Server databases1434 = rounded volume of a regular tetrahedron with edge length 23[251]1435 = vampire number;[171] the standard railway gauge in millimetres, equivalent to 4 feet <span class="frac" role="math">8<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">2</span></span>&nbsp;inches (1.435&nbsp;m)</dd> <dd><b>1437</b> = smallest number of complexity 20: smallest number requiring 20 1's to build using +, * and ^<sup id="cite_ref-252" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-252">[252]</a></sup></dd> <dd><b>1438</b> = k such that 5 × 2<sup>k</sup> - 1 is prime<sup id="cite_ref-253" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-253">[253]</a></sup></dd> <dd><b>1439</b> = Sophie Germain prime,<sup id="cite_ref-Sophie_Germain_11-9" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Sophie_Germain-11">[11]</a></sup> safe prime<sup id="cite_ref-Safe_primes_19-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Safe_primes-19">[19]</a></sup></dd> <dd><b>1440</b> = a <a target="_blank" href="https://en.wikipedia.org/wiki/Highly_totient_number" title="Highly totient number">highly totient number</a><sup id="cite_ref-highly_totient_120-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-highly_totient-120">[120]</a></sup> and a 481-<a target="_blank" href="https://en.wikipedia.org/wiki/Polygonal_number" title="Polygonal number">gonal number</a>. Also, the number of <a target="_blank" href="https://en.wikipedia.org/wiki/Minute" title="Minute">minutes</a> in one day, the blocksize of a standard <style data-mw-deduplicate="TemplateStyles:r1050945101">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}<span role="math" class="sfrac">3<span class="sr-only">+</span><span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span></span> <a target="_blank" href="https://en.wikipedia.org/wiki/Floppy_disk" title="Floppy disk">floppy disk</a>, and the horizontal resolution of <a target="_blank" href="https://en.wikipedia.org/wiki/WSXGA_Wide_XGA%2B" class="mw-redirect" title="WSXGA Wide XGA+">WXGA(II)</a> computer displays</dd> <dd><b>1441</b> = star number<sup id="cite_ref-Centered_12-gonal_numbers_80-2" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_12-gonal_numbers-80">[80]</a></sup></dd> <dd><b>1442</b> = number of parts in all partitions of 31 into distinct parts<sup id="cite_ref-254" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-254">[254]</a></sup></dd> <dd><b>1443</b> = the sum of the second trio of three-digit <a target="_blank" href="https://en.wikipedia.org/wiki/Permutable_prime" title="Permutable prime">permutable primes</a> in <a target="_blank" href="https://en.wikipedia.org/wiki/Decimal" title="Decimal">decimal</a>: <a target="_blank" href="https://en.wikipedia.org/wiki/337_(number)" class="mw-redirect" title="337 (number)">337</a>, <a target="_blank" href="https://en.wikipedia.org/wiki/373_(number)" class="mw-redirect" title="373 (number)">373</a>, and <a target="_blank" href="https://en.wikipedia.org/wiki/733_(number)" class="mw-redirect" title="733 (number)">733</a>. Also the number of edges in the join of two cycle graphs, both of order <a target="_blank" href="https://en.wikipedia.org/wiki/37_(number)" title="37 (number)">37</a><sup id="cite_ref-255" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-255">[255]</a></sup></dd> <dd><b>1444</b> = 38<sup>2</sup>, smallest <a target="_blank" href="https://en.wikipedia.org/wiki/Pandigital_number" title="Pandigital number">pandigital number</a> in <a target="_blank" href="https://en.wikipedia.org/wiki/Roman_numerals" title="Roman numerals">Roman numerals</a></dd> <dd><b>1446</b> = number of points on surface of octahedron with edgelength 19<sup id="cite_ref-256" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-256">[256]</a></sup></dd> <dd><b>1447</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a>, <a target="_blank" href="https://en.wikipedia.org/wiki/Happy_number" title="Happy number">happy number</a></dd> <dd><b>1448</b> = number k such that phi(prime(k)) is a square<sup id="cite_ref-257" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-257">[257]</a></sup></dd> <dd><b>1449</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Stella_octangula_number" title="Stella octangula number">Stella octangula number</a></dd> <dd><b>1450</b> = σ<sub>2</sub>(34): sum of squares of divisors of 34<sup id="cite_ref-258" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-258">[258]</a></sup></dd> <dd><b>1451</b> = Sophie Germain prime<sup id="cite_ref-Sophie_Germain_11-10" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Sophie_Germain-11">[11]</a></sup></dd> <dd><b>1452</b> = first Zagreb index of the complete graph K<sub>12</sub><sup id="cite_ref-259" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-259">[259]</a></sup></dd> <dd><b>1453</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Sexy_prime" title="Sexy prime">Sexy prime</a> with 1459</dd> <dd><b>1454</b> = 3 × 22<sup>2</sup> + 2 = number of points on surface of square pyramid of side-length 22<sup id="cite_ref-260" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-260">[260]</a></sup></dd> <dd><b>1455</b> = k such that geometric mean of phi(k) and sigma(k) is an integer<sup id="cite_ref-261" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-261">[261]</a></sup></dd> <dd><b>1457</b> = 2 × 27<sup>2</sup> − 1 = a <a target="_blank" rel="nofollow" class="external text" href="https://oeis.org/A056220/a056220.jpg">twin square</a><sup id="cite_ref-262" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-262">[262]</a></sup></dd> <dd><b><a target="_blank" href="https://en.wikipedia.org/wiki/1458_(number)" title="1458 (number)">1458</a></b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Hadamard%27s_maximal_determinant_problem" title="Hadamard's maximal determinant problem">maximum determinant</a> of an 11 by 11 matrix of zeroes and ones, <a target="_blank" href="https://en.wikipedia.org/wiki/3-smooth" class="mw-redirect" title="3-smooth">3-smooth</a> number (2×3<sup>6</sup>)</dd> <dd><b>1459</b> = Sexy prime with 1453, sum of nine consecutive primes (139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181), <a target="_blank" href="https://en.wikipedia.org/wiki/Pierpont_prime" title="Pierpont prime">pierpont prime</a></dd> <dd><b>1460</b> = Nickname of the original "<a target="_blank" href="https://en.wikipedia.org/wiki/Doc_Marten%27s" class="mw-redirect" title="Doc Marten's">Doc Marten's</a>" boots, released 1 April 1960</dd> <dd><b>1461</b> = number of partitions of 38 into prime power parts<sup id="cite_ref-263" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-263">[263]</a></sup></dd> <dd><b>1462</b> = (35 - 1) × (35 + 8) = the first Zagreb index of the wheel graph with 35 vertices<sup id="cite_ref-264" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-264">[264]</a></sup></dd> <dd><b>1463</b> = total number of parts in all partitions of 16<sup id="cite_ref-265" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-265">[265]</a></sup></dd> <dd><b>1464</b> = rounded total surface area of a regular icosahedron with edge length 13<sup id="cite_ref-266" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-266">[266]</a></sup></dd> <dd><b>1465</b> = 5-<a target="_blank" href="https://en.wikipedia.org/wiki/Kn%C3%B6del_number" title="Knödel number">Knödel number</a><sup id="cite_ref-267" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-267">[267]</a></sup></dd> <dd><b>1469</b> = octahedral number,<sup id="cite_ref-Octahedral_number_124-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Octahedral_number-124">[124]</a></sup> highly cototient number<sup id="cite_ref-highly_cototient_40-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-highly_cototient-40">[40]</a></sup></dd> <dd><b>1470</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Pentagonal_pyramidal_number" class="mw-redirect" title="Pentagonal pyramidal number">pentagonal pyramidal number</a>,<sup id="cite_ref-Pentagonal_pyramidal_number_268-0" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pentagonal_pyramidal_number-268">[268]</a></sup> sum of totient function for first 69 integers</dd> <dd><b>1471</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a>, centered heptagonal number<sup id="cite_ref-centered_heptagonal_number_63-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-centered_heptagonal_number-63">[63]</a></sup></dd> <dd><b>1473</b> = <a target="_blank" rel="nofollow" class="external text" href="https://oeis.org/A144391/a144391.jpg">cropped hexagone</a><sup id="cite_ref-269" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-269">[269]</a></sup></dd> <dd><b>1476</b> = coreful perfect number<sup id="cite_ref-270" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-270">[270]</a></sup></dd> <dd><b>1477</b> = 7-Knödel number<sup id="cite_ref-271" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-271">[271]</a></sup></dd> <dd><b>1479</b> = number of planar partitions of 12<sup id="cite_ref-272" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-272">[272]</a></sup></dd> <dd><b>1480</b> = sum of the first 29 primes</dd> <dd><b>1481</b> = Sophie Germain prime<sup id="cite_ref-Sophie_Germain_11-11" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Sophie_Germain-11">[11]</a></sup></dd> <dd><b>1482</b> = pronic number,<sup id="cite_ref-pronic_number_48-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-pronic_number-48">[48]</a></sup> number of unimodal compositions of 15 where the maximal part appears once<sup id="cite_ref-273" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-273">[273]</a></sup></dd> <dd><b>1483</b> = 39<sup>2</sup> - 39 + 1 = H<sub>39</sub> (the 39th Hogben number)<sup id="cite_ref-274" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-274">[274]</a></sup></dd> <dd><b>1484</b> = maximal number of regions the plane is divided into by drawing 39 circles<sup id="cite_ref-275" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-275">[275]</a></sup></dd> <dd><b>1485</b> = triangular number</dd> <dd><b>1486</b> = number of strict solid partitions of 19<sup id="cite_ref-276" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-276">[276]</a></sup></dd> <dd><b>1487</b> = safe prime<sup id="cite_ref-Safe_primes_19-7" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Safe_primes-19">[19]</a></sup></dd> <dd><b>1488</b> = triangular matchstick number<sup id="cite_ref-auto5_45-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-auto5-45">[45]</a></sup></dd> <dd><b>1489</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Centered_triangular_number" title="Centered triangular number">centered triangular number</a><sup id="cite_ref-277" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-277">[277]</a></sup></dd> <dd><b>1490</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Tetranacci_number" class="mw-redirect" title="Tetranacci number">tetranacci number</a><sup id="cite_ref-278" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-278">[278]</a></sup></dd> <dd><b>1491</b> = nonagonal number,<sup id="cite_ref-Nonagonal_number_151-2" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Nonagonal_number-151">[151]</a></sup> Mertens function zero</dd> <dd><b>1492</b> = Mertens function zero</dd> <dd><b>1493</b> = Stern prime<sup id="cite_ref-Stern_prime_137-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Stern_prime-137">[137]</a></sup></dd> <dd><b>1494</b> = sum of totient function for first 70 integers</dd> <dd><b>1496</b> = square pyramidal number<sup id="cite_ref-Square_pyramidal_numbers_14-2" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Square_pyramidal_numbers-14">[14]</a></sup></dd> <dd><b>1497</b> = skiponacci number<sup id="cite_ref-279" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-279">[279]</a></sup></dd> <dd><b>1498</b> = number of flat partitions of 41<sup id="cite_ref-280" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-280">[280]</a></sup></dd> <dd><b>1499</b> = Sophie Germain prime,<sup id="cite_ref-Sophie_Germain_11-12" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Sophie_Germain-11">[11]</a></sup> <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a></dd></dl> <h3><span class="mw-headline" id="1500_to_1599">1500 to 1599</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a target="_blank" href="https://en.wikipedia.org/w/index.php?title=1000_(number)&action=edit§ion=9" title="Edit section: 1500 to 1599">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <dl><dd><b>1500</b> = hypotenuse in three different Pythagorean triangles<sup id="cite_ref-281" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-281">[281]</a></sup></dd> <dd><b>1501</b> = centered pentagonal number<sup id="cite_ref-Centered_pentagonal_43-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_pentagonal-43">[43]</a></sup></dd> <dd><b>1502</b> = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 47<sup id="cite_ref-282" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-282">[282]</a></sup></dd> <dd><b>1504</b> = primitive abundant number (<a target="_blank" href="https://en.wikipedia.org/wiki/Abundant_number" title="Abundant number">abundant number</a> all of whose proper divisors are <a target="_blank" href="https://en.wikipedia.org/wiki/Deficient_numbers" class="mw-redirect" title="Deficient numbers">deficient numbers</a>)<sup id="cite_ref-283" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-283">[283]</a></sup></dd> <dd><b>1507</b> = number of partitions of 32 that do not contain 1 as a part<sup id="cite_ref-auto8_31-2" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-auto8-31">[31]</a></sup></dd> <dd><b>1508</b> = heptagonal pyramidal number<sup id="cite_ref-284" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-284">[284]</a></sup></dd> <dd><b>1509</b> = pinwheel number<sup id="cite_ref-Pinwheel_87-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pinwheel-87">[87]</a></sup></dd> <dd><b><a target="_blank" href="https://en.wikipedia.org/wiki/1510_(number)" title="1510 (number)">1510</a></b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Deficient_number" title="Deficient number">deficient number</a>, <a target="_blank" href="https://en.wikipedia.org/wiki/Odious_number" title="Odious number">odious number</a></dd> <dd><b>1511</b> = Sophie Germain prime,<sup id="cite_ref-Sophie_Germain_11-13" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Sophie_Germain-11">[11]</a></sup> balanced prime<sup id="cite_ref-Balanced_prime_88-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Balanced_prime-88">[88]</a></sup></dd> <dd><b>1512</b> = k such that geometric mean of phi(k) and sigma(k) is an integer<sup id="cite_ref-285" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-285">[285]</a></sup></dd> <dd><b>1513</b> = centered square number<sup id="cite_ref-Centered_square_numbers_12-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_square_numbers-12">[12]</a></sup></dd> <dd><b>1514</b> = sum of first 44 composite numbers<sup id="cite_ref-286" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-286">[286]</a></sup></dd> <dd><b>1517</b> = number of lattice points inside a circle of radius 22<sup id="cite_ref-287" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-287">[287]</a></sup></dd> <dd><b>1518</b> = Mertens function zero</dd> <dd><b>1519</b> = Mertens function zero</dd> <dd><b>1520</b> = pentagonal number,<sup id="cite_ref-Pentagonal_number_67-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pentagonal_number-67">[67]</a></sup> Mertens function zero, forms a Ruth–Aaron pair with 1521 under second definition</dd> <dd><b>1521</b> = 39<sup>2</sup>, Mertens function zero, centered octagonal number,<sup id="cite_ref-Centered_octagonal_number_156-2" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_octagonal_number-156">[156]</a></sup> forms a Ruth–Aaron pair with 1520 under second definition</dd> <dd><b>1522</b> = k such that 5 × 2<sup>k</sup> - 1 is prime<sup id="cite_ref-288" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-288">[288]</a></sup></dd> <dd><b>1523</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a>, Mertens function zero, safe prime,<sup id="cite_ref-Safe_primes_19-8" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Safe_primes-19">[19]</a></sup> member of the Mian–Chowla sequence<sup id="cite_ref-Mian-Chowla_15-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Mian-Chowla-15">[15]</a></sup></dd> <dd><b>1524</b> = Mertens function zero, k such that geometric mean of phi(k) and sigma(k) is an integer<sup id="cite_ref-289" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-289">[289]</a></sup></dd> <dd><b>1525</b> = heptagonal number,<sup id="cite_ref-heptagonal_number_62-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-heptagonal_number-62">[62]</a></sup> Mertens function zero</dd> <dd><b>1526</b> = number of conjugacy classes in the alternating group A<sub>27</sub><sup id="cite_ref-290" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-290">[290]</a></sup></dd> <dd><b>1527</b> = Mertens function zero</dd> <dd><b>1528</b> = Mertens function zero, rounded total surface area of a regular octahedron with edge length 21<sup id="cite_ref-291" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-291">[291]</a></sup></dd> <dd><b>1529</b> = composite <a target="_blank" href="https://en.wikipedia.org/wiki/De_Polignac_number" class="mw-redirect" title="De Polignac number">de Polignac number</a><sup id="cite_ref-292" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-292">[292]</a></sup></dd> <dd><b>1530</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Vampire_number" title="Vampire number">vampire number</a><sup id="cite_ref-Vampire_number_171-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Vampire_number-171">[171]</a></sup></dd> <dd><b>1531</b> = prime number, <a target="_blank" href="https://en.wikipedia.org/wiki/Centered_decagonal_number" title="Centered decagonal number">centered decagonal number</a>, Mertens function zero</dd> <dd><b>1532</b> = Mertens function zero</dd> <dd><b>1534</b> = number of achiral integer partitions of 50<sup id="cite_ref-293" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-293">[293]</a></sup></dd> <dd><b>1535</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Thabit_number" title="Thabit number">Thabit number</a></dd> <dd><b>1536</b> = a common size of <a target="_blank" href="https://en.wikipedia.org/wiki/Microplate" title="Microplate">microplate</a>, <a target="_blank" href="https://en.wikipedia.org/wiki/3-smooth" class="mw-redirect" title="3-smooth">3-smooth</a> number (2<sup>9</sup>×3), number of threshold functions of exactly 4 variables<sup id="cite_ref-294" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-294">[294]</a></sup></dd> <dd><b>1537</b> = Keith number,<sup id="cite_ref-Keith_number_89-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Keith_number-89">[89]</a></sup> Mertens function zero</dd> <dd><b>1538</b> = number of surface points on a cube with edge-length 17<sup id="cite_ref-A005897_16-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-A005897-16">[16]</a></sup></dd> <dd><b>1539</b> = maximal number of pieces that can be obtained by cutting an annulus with 54 cuts<sup id="cite_ref-295" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-295">[295]</a></sup></dd> <dd><b>1540</b> = triangular number, hexagonal number,<sup id="cite_ref-Hexagonal_number_26-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Hexagonal_number-26">[26]</a></sup> decagonal number,<sup id="cite_ref-Decagonal_91-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Decagonal-91">[91]</a></sup> tetrahedral number<sup id="cite_ref-Leyland_number_105-2" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Leyland_number-105">[105]</a></sup></dd> <dd><b>1541</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Octagonal_number" title="Octagonal number">octagonal number</a><sup id="cite_ref-296" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-296">[296]</a></sup></dd> <dd><b>1543</b> = Mertens function zero</dd> <dd><b>1544</b> = Mertens function zero, number of partitions of integer partitions of 17 where all parts have the same length<sup id="cite_ref-297" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-297">[297]</a></sup></dd> <dd><b>1546</b> = Mertens function zero</dd> <dd><b>1547</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Hexagonal_pyramidal_number" class="mw-redirect" title="Hexagonal pyramidal number">hexagonal pyramidal number</a></dd> <dd><b>1548</b> = coreful perfect number<sup id="cite_ref-298" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-298">[298]</a></sup></dd> <dd><b>1549</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/De_Polignac_number" class="mw-redirect" title="De Polignac number">de Polignac</a> prime<sup id="cite_ref-299" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-299">[299]</a></sup></dd> <dd><b>1552</b> = <a target="_blank" href="https://oeis.org/A000607" class="extiw" title="oeis:A000607">Number of partitions of 57 into prime parts</a></dd> <dd><b>1556</b> = sum of the squares of the first nine primes</dd> <dd><b>1557</b> = number of graphs with 8 nodes and 13 edges<sup id="cite_ref-300" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-300">[300]</a></sup></dd> <dd><b>1558</b> = <a target="_blank" href="https://oeis.org/A006316" class="extiw" title="oeis:A006316">number k</a> such that k<sup>64</sup> + 1 is prime</dd> <dd><b>1559</b> = Sophie Germain prime<sup id="cite_ref-Sophie_Germain_11-14" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Sophie_Germain-11">[11]</a></sup></dd> <dd><b>1560</b> = pronic number<sup id="cite_ref-pronic_number_48-7" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-pronic_number-48">[48]</a></sup></dd> <dd><b>1561</b> = a <a target="_blank" href="https://en.wikipedia.org/wiki/Centered_octahedral_number" title="Centered octahedral number">centered octahedral number</a>,<sup id="cite_ref-auto7_127-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-auto7-127">[127]</a></sup> number of series-reduced trees with 19 nodes<sup id="cite_ref-301" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-301">[301]</a></sup></dd> <dd><b>1562</b> = maximal number of regions the plane is divided into by drawing 40 circles<sup id="cite_ref-302" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-302">[302]</a></sup></dd> <dd><b>1564</b> = sum of totient function for first 71 integers</dd> <dd><b>1565</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {1036^{2}+1173^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mn>1036</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>1173</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {1036^{2}+1173^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc14906aac83dc79cfa91f76e67322c864c116a4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-0.838ex;width:16.572ex;height:3.509ex" alt="{\displaystyle {\sqrt {1036^{2}+1173^{2}}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1036+1173=47^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1036</mn> <mo>+</mo> <mn>1173</mn> <mo>=</mo> <msup> <mn>47</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1036+1173=47^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04441f3b13db70bcbe1c7141ac7f75e10134317c" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-0.505ex;width:18.618ex;height:2.843ex" alt="{\displaystyle 1036+1173=47^{2}}"></span><sup id="cite_ref-303" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-303">[303]</a></sup></dd> <dd><b>1566</b> = <a target="_blank" href="https://oeis.org/A006316" class="extiw" title="oeis:A006316">number k</a> such that k<sup>64</sup> + 1 is prime</dd> <dd><b>1567</b> = number of partitions of 24 with at least one distinct part<sup id="cite_ref-304" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-304">[304]</a></sup></dd> <dd><b>1568</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Achilles_number" title="Achilles number">Achilles number</a><sup id="cite_ref-Achilles_305-0" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Achilles-305">[305]</a></sup></dd> <dd><b>1569</b> = 2 × 28<sup>2</sup> + 1 = number of different 2 × 2 determinants with integer entries from 0 to 28<sup id="cite_ref-306" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-306">[306]</a></sup></dd> <dd><b>1570</b> = 2 × 28<sup>2</sup> + 2 = number of points on surface of tetrahedron with edgelength 28<sup id="cite_ref-307" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-307">[307]</a></sup></dd> <dd><b>1571</b> = Honaker prime<sup id="cite_ref-308" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-308">[308]</a></sup></dd> <dd><b>1572</b> = member of the Mian–Chowla sequence<sup id="cite_ref-Mian-Chowla_15-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Mian-Chowla-15">[15]</a></sup></dd> <dd><b>1575</b> = odd <a target="_blank" href="https://en.wikipedia.org/wiki/Abundant_number" title="Abundant number">abundant number</a>,<sup id="cite_ref-309" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-309">[309]</a></sup> <a target="_blank" href="https://oeis.org/A006002" class="extiw" title="oeis:A006002">sum of the nontriangular numbers between successive triangular numbers</a>, number of partitions of 24<sup id="cite_ref-310" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-310">[310]</a></sup></dd> <dd><b>1578</b> = sum of first 45 composite numbers<sup id="cite_ref-311" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-311">[311]</a></sup></dd> <dd><b>1579</b> = number of partitions of 54 such that the smallest part is greater than or equal to number of parts<sup id="cite_ref-312" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-312">[312]</a></sup></dd> <dd><b>1580</b> = number of achiral integer partitions of 51<sup id="cite_ref-313" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-313">[313]</a></sup></dd> <dd><b>1581</b> = number of edges in the <a target="_blank" href="https://en.wikipedia.org/wiki/File:Hexagonal_triangle.png" title="File:Hexagonal triangle.png">hexagonal triangle</a> T(31)<sup id="cite_ref-314" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-314">[314]</a></sup></dd> <dd><b>1583</b> = Sophie Germain prime</dd> <dd><b>1584</b> = triangular matchstick number<sup id="cite_ref-auto5_45-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-auto5-45">[45]</a></sup></dd> <dd><b>1585</b> = <a target="_blank" href="https://oeis.org/A005043" class="extiw" title="oeis:A005043">Riordan number</a>, <a target="_blank" href="https://en.wikipedia.org/wiki/Centered_triangular_number" title="Centered triangular number">centered triangular number</a><sup id="cite_ref-315" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-315">[315]</a></sup></dd> <dd><b>1586</b> = area of the 23th <a target="_blank" rel="nofollow" class="external text" href="https://oeis.org/A080663/a080663.jpg">conjoined trapezoid</a><sup id="cite_ref-316" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-316">[316]</a></sup></dd> <dd><b>1588</b> = sum of totient function for first 72 integers</dd> <dd><b>1589</b> = composite <a target="_blank" href="https://en.wikipedia.org/wiki/De_Polignac_number" class="mw-redirect" title="De Polignac number">de Polignac number</a><sup id="cite_ref-317" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-317">[317]</a></sup></dd> <dd><b>1590</b> = rounded volume of a regular icosahedron with edge length 9<sup id="cite_ref-318" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-318">[318]</a></sup></dd> <dd><b>1591</b> = rounded volume of a regular octahedron with edge length 15<sup id="cite_ref-319" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-319">[319]</a></sup></dd> <dd><b>1593</b> = sum of the first 30 primes</dd> <dd><b>1595</b> = <a target="_blank" href="https://oeis.org/A283877" class="extiw" title="oeis:A283877">number of non-isomorphic set-systems of weight 10</a></dd> <dd><b>1596</b> = triangular number</dd> <dd><b>1597</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Fibonacci_prime" title="Fibonacci prime">Fibonacci prime</a>,<sup id="cite_ref-320" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-320">[320]</a></sup> <a target="_blank" href="https://en.wikipedia.org/wiki/Markov_prime" class="mw-redirect" title="Markov prime">Markov prime</a>,<sup id="cite_ref-Markov_number_198-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Markov_number-198">[198]</a></sup> <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a>, <a target="_blank" href="https://en.wikipedia.org/wiki/Emirp" title="Emirp">emirp</a></dd> <dd><b>1598</b> = number of unimodular 2 × 2 matrices having all terms in {0,1,...,25}<sup id="cite_ref-321" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-321">[321]</a></sup></dd> <dd><b>1599</b> = number of edges in the join of two cycle graphs, both of order 39<sup id="cite_ref-322" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-322">[322]</a></sup></dd></dl> <h3><span class="mw-headline" id="1600_to_1699">1600 to 1699</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a target="_blank" href="https://en.wikipedia.org/w/index.php?title=1000_(number)&action=edit§ion=10" title="Edit section: 1600 to 1699">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <dl><dd><b>1600</b> = 40<sup>2</sup>, structured great rhombicosidodecahedral number,<sup id="cite_ref-323" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-323">[323]</a></sup> repdigit in base 7 (4444<sub>7</sub>), street number on Pennsylvania Avenue of the <a target="_blank" href="https://en.wikipedia.org/wiki/White_House" title="White House">White House</a>, length in meters of a common High School Track Event, perfect score on <a target="_blank" href="https://en.wikipedia.org/wiki/SAT" title="SAT">SAT</a> (except from 2005-2015)</dd> <dd><b>1601</b> = Sophie Germain prime, Proth prime,<sup id="cite_ref-Proth_prime_121-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Proth_prime-121">[121]</a></sup> the novel <i><a target="_blank" href="https://en.wikipedia.org/wiki/1601_(Mark_Twain)" title="1601 (Mark Twain)">1601 (Mark Twain)</a></i></dd> <dd><b>1602</b> = number of points on surface of octahedron with edgelength 20<sup id="cite_ref-324" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-324">[324]</a></sup></dd> <dd><b>1603</b> = number of partitions of 27 with nonnegative rank<sup id="cite_ref-325" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-325">[325]</a></sup></dd> <dd><b>1606</b> = enneagonal pyramidal number<sup id="cite_ref-326" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-326">[326]</a></sup></dd> <dd><b>1608</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{k=1}^{44}\sigma (k)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>44</mn> </mrow> </munderover> <mi>σ</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=1}^{44}\sigma (k)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab6ae50102b59af07a720daea47de6f8ef0f784f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-3.005ex;width:8.092ex;height:7.343ex" alt="{\displaystyle \sum _{k=1}^{44}\sigma (k)}"></span><sup id="cite_ref-327" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-327">[327]</a></sup></dd> <dd><b>1609</b> = <a target="_blank" rel="nofollow" class="external text" href="https://oeis.org/A144391/a144391.jpg">cropped hexagone</a><sup id="cite_ref-328" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-328">[328]</a></sup></dd> <dd><b>1610</b> = number of strict partions of 43<sup id="cite_ref-329" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-329">[329]</a></sup></dd> <dd><b>1611</b> = number of rational numbers which can be constructed from the set of integers between 1 and 51<sup id="cite_ref-330" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-330">[330]</a></sup></dd> <dd><b>1617</b> = pentagonal number<sup id="cite_ref-Pentagonal_number_67-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pentagonal_number-67">[67]</a></sup></dd> <dd><b>1618</b> = centered heptagonal number<sup id="cite_ref-centered_heptagonal_number_63-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-centered_heptagonal_number-63">[63]</a></sup></dd> <dd><b>1619</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Palindromic_prime" title="Palindromic prime">palindromic prime</a> in <a target="_blank" href="https://en.wikipedia.org/wiki/Binary_numeral_system" class="mw-redirect" title="Binary numeral system">binary</a>, safe prime<sup id="cite_ref-Safe_primes_19-9" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Safe_primes-19">[19]</a></sup></dd> <dd><b>1620</b> = 809 + 811: sum of twin prime pair<sup id="cite_ref-331" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-331">[331]</a></sup></dd> <dd><b>1621</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a>, pinwheel number<sup id="cite_ref-Pinwheel_87-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pinwheel-87">[87]</a></sup></dd> <dd><b>1624</b> = number of squares in the <a target="_blank" href="https://en.wikipedia.org/wiki/Aztec_diamond" title="Aztec diamond">Aztec diamond</a> of order 28<sup id="cite_ref-332" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-332">[332]</a></sup></dd> <dd><b>1625</b> = centered square number<sup id="cite_ref-Centered_square_numbers_12-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_square_numbers-12">[12]</a></sup></dd> <dd><b>1626</b> = centered pentagonal number<sup id="cite_ref-Centered_pentagonal_43-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_pentagonal-43">[43]</a></sup></dd> <dd><b>1629</b> = rounded volume of a regular tetrahedron with edge length 24<sup id="cite_ref-333" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-333">[333]</a></sup></dd> <dd><b>1630</b> = <a target="_blank" href="https://oeis.org/A006316" class="extiw" title="oeis:A006316">number k such that k^64 + 1 is prime</a></dd> <dd><b>1633</b> = star number<sup id="cite_ref-Centered_12-gonal_numbers_80-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_12-gonal_numbers-80">[80]</a></sup></dd> <dd><b>1634</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Narcissistic_number" title="Narcissistic number">Narcissistic number</a> in base 10</dd> <dd><b>1636</b> = number of nonnegative solutions to x<sup>2</sup> + y<sup>2</sup> ≤ 45<sup>2</sup><sup id="cite_ref-334" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-334">[334]</a></sup></dd> <dd><b>1637</b> = prime island: least prime whose adjacent primes are exactly 30 apart<sup id="cite_ref-335" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-335">[335]</a></sup></dd> <dd><b>1638</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Harmonic_divisor_number" title="Harmonic divisor number">harmonic divisor number</a>,<sup id="cite_ref-336" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-336">[336]</a></sup> 5 × 2<sup>1638</sup> - 1 is prime<sup id="cite_ref-337" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-337">[337]</a></sup></dd> <dd><b>1639</b> = nonagonal number<sup id="cite_ref-Nonagonal_number_151-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Nonagonal_number-151">[151]</a></sup></dd> <dd><b>1640</b> = pronic number<sup id="cite_ref-pronic_number_48-8" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-pronic_number-48">[48]</a></sup></dd> <dd><b>1641</b> = 41<sup>2</sup> - 41 + 1 = H<sub>41</sub> (the 41st Hogben number)<sup id="cite_ref-338" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-338">[338]</a></sup></dd> <dd><b>1642</b> = maximal number of regions the plane is divided into by drawing 41 circles<sup id="cite_ref-339" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-339">[339]</a></sup></dd> <dd><b>1643</b> = sum of first 46 composite numbers<sup id="cite_ref-340" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-340">[340]</a></sup></dd> <dd><b>1644</b> = 821 + 823: sum of twin prime pair<sup id="cite_ref-341" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-341">[341]</a></sup></dd> <dd><b>1645</b> = number of 16-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection<sup id="cite_ref-342" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-342">[342]</a></sup></dd> <dd><b>1646</b> = number of graphs with 8 nodes and 14 edges<sup id="cite_ref-343" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-343">[343]</a></sup></dd> <dd><b>1647</b> and 1648 are both divisible by cubes<sup id="cite_ref-344" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-344">[344]</a></sup></dd> <dd><b>1648</b> = number of partitions of 34<sup>3</sup> into distinct cubes<sup id="cite_ref-345" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-345">[345]</a></sup></dd> <dd><b>1649</b> = highly cototient number,<sup id="cite_ref-highly_cototient_40-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-highly_cototient-40">[40]</a></sup> Leyland number<sup id="cite_ref-Leyland_number_105-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Leyland_number-105">[105]</a></sup></dd> <dd><b>1650</b> = number of cards to build an 33-tier house of cards<sup id="cite_ref-346" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-346">[346]</a></sup></dd> <dd><b>1651</b> = heptagonal number<sup id="cite_ref-heptagonal_number_62-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-heptagonal_number-62">[62]</a></sup></dd> <dd><b>1652</b> = number of partitions of 29 into a prime number of parts<sup id="cite_ref-347" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-347">[347]</a></sup></dd> <dd><b>1653</b> = triangular number, hexagonal number,<sup id="cite_ref-Hexagonal_number_26-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Hexagonal_number-26">[26]</a></sup> number of lattice points inside a circle of radius 23<sup id="cite_ref-348" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-348">[348]</a></sup></dd> <dd><b>1654</b> = number of partitions of 42 into divisors of 42<sup id="cite_ref-349" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-349">[349]</a></sup></dd> <dd><b>1655</b> = rounded volume of a regular dodecahedron with edge length 6<sup id="cite_ref-350" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-350">[350]</a></sup></dd> <dd><b>1656</b> = 827 + 829: sum of twin prime pair<sup id="cite_ref-351" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-351">[351]</a></sup></dd> <dd><b>1657</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Cuban_prime" title="Cuban prime">cuban prime</a>,<sup id="cite_ref-Cuban_Prime_352-0" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Cuban_Prime-352">[352]</a></sup> prime of the form 2p-1</dd> <dd><b>1658</b> = smallest composite that when added to sum of prime factors reaches a prime after 25 iterations<sup id="cite_ref-353" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-353">[353]</a></sup></dd> <dd><b>1659</b> = number of rational numbers which can be constructed from the set of integers between 1 and 52<sup id="cite_ref-354" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-354">[354]</a></sup></dd> <dd><b>1660</b> = sum of totient function for first 73 integers</dd> <dd><b>1661</b> = a number with only palindromic divisors<sup id="cite_ref-355" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-355">[355]</a></sup></dd> <dd><b>1662</b> = number of partitions of 49 into pairwise relatively prime parts<sup id="cite_ref-356" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-356">[356]</a></sup></dd> <dd><b>1663</b> = a prime number and 5<sup>1663</sup> - 4<sup>1663</sup> is a 1163-digit prime number<sup id="cite_ref-357" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-357">[357]</a></sup></dd> <dd><b>1664</b> = k such that k, k+1 and k+2 are sums of 2 squares<sup id="cite_ref-358" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-358">[358]</a></sup></dd> <dd><b>1665</b> = centered tetrahedral number<sup id="cite_ref-359" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-359">[359]</a></sup></dd> <dd><b>1666</b> = largest efficient <a target="_blank" href="https://en.wikipedia.org/wiki/Pandigital_number" title="Pandigital number">pandigital number</a> in <a target="_blank" href="https://en.wikipedia.org/wiki/Roman_numerals" title="Roman numerals">Roman numerals</a> (each symbol occurs exactly once)</dd> <dd><b>1667</b> = 228 + 1439 and the 228th prime is 1439<sup id="cite_ref-360" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-360">[360]</a></sup></dd> <dd><b>1668</b> = number of partitions of 33 into parts all relatively prime to 33<sup id="cite_ref-361" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-361">[361]</a></sup></dd> <dd><b>1669</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a>, smallest prime with a gap of exactly 24 to the next prime<sup id="cite_ref-362" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-362">[362]</a></sup></dd> <dd><b>1670</b> = number of compositions of 12 such that at least two adjacent parts are equal<sup id="cite_ref-363" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-363">[363]</a></sup></dd> <dd><b>1671</b> divides the sum of the first 1671 composite numbers<sup id="cite_ref-364" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-364">[364]</a></sup></dd> <dd><b>1672</b> = 41<sup>2</sup> - 2<sup>2</sup>, the only way to express 1672 as a difference of prime squares<sup id="cite_ref-365" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-365">[365]</a></sup></dd> <dd><b>1673</b> = RMS number<sup id="cite_ref-366" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-366">[366]</a></sup></dd> <dd><b>1674</b> = k such that geometric mean of phi(k) and sigma(k) is an integer<sup id="cite_ref-367" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-367">[367]</a></sup></dd> <dd><b>1675</b> = Kin number<sup id="cite_ref-368" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-368">[368]</a></sup></dd> <dd><b>1676</b> = number of partitions of 34 into parts each of which is used a different number of times<sup id="cite_ref-369" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-369">[369]</a></sup></dd> <dd><b>1677</b> = 41<sup>2</sup> - 3<sup>2</sup>, the only way to express 1677 as a difference of prime squares<sup id="cite_ref-370" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-370">[370]</a></sup></dd> <dd><b>1678</b> = n such that n<sup>32</sup> + 1 is prime<sup id="cite_ref-371" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-371">[371]</a></sup></dd> <dd><b>1679</b> = highly cototient number,<sup id="cite_ref-highly_cototient_40-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-highly_cototient-40">[40]</a></sup> semiprime (23 × 73, see also <a target="_blank" href="https://en.wikipedia.org/wiki/Arecibo_message" title="Arecibo message">Arecibo message</a>), number of parts in all partitions of 32 into distinct parts<sup id="cite_ref-372" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-372">[372]</a></sup></dd> <dd><b>1680</b> = highly composite number,<sup id="cite_ref-Highly_composite_170-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Highly_composite-170">[170]</a></sup> number of edges in the join of two cycle graphs, both of order 40<sup id="cite_ref-373" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-373">[373]</a></sup></dd> <dd><b>1681</b> = 41<sup>2</sup>, smallest number yielded by the formula <i>n</i><sup>2</sup> + <i>n</i> + 41 that is not a prime; centered octagonal number<sup id="cite_ref-Centered_octagonal_number_156-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_octagonal_number-156">[156]</a></sup></dd> <dd><b>1682</b> = and <b>1683</b> is a member of a Ruth–Aaron pair (first definition)</dd> <dd><b>1683</b> = triangular matchstick number<sup id="cite_ref-auto5_45-7" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-auto5-45">[45]</a></sup></dd> <dd><b>1684</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Centered_triangular_number" title="Centered triangular number">centered triangular number</a><sup id="cite_ref-374" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-374">[374]</a></sup></dd> <dd><b>1685</b> = 5-<a target="_blank" href="https://en.wikipedia.org/wiki/Kn%C3%B6del_number" title="Knödel number">Knödel number</a><sup id="cite_ref-375" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-375">[375]</a></sup></dd> <dd><b>1686</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{k=1}^{45}\sigma (k)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>45</mn> </mrow> </munderover> <mi>σ</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=1}^{45}\sigma (k)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10a50c99f28832c93d82a2f72897ae267ce4e320" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-3.005ex;width:8.092ex;height:7.343ex" alt="{\displaystyle \sum _{k=1}^{45}\sigma (k)}"></span><sup id="cite_ref-376" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-376">[376]</a></sup></dd> <dd><b>1687</b> = 7-Knödel number<sup id="cite_ref-377" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-377">[377]</a></sup></dd> <dd><b>1688</b> = number of finite connected sets of positive integers greater than one with least common multiple 72<sup id="cite_ref-378" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-378">[378]</a></sup></dd> <dd><b>1689</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 9!!\sum _{k=0}^{4}{\frac {1}{2k+1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>9</mn> <mo>!</mo> <mo>!</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 9!!\sum _{k=0}^{4}{\frac {1}{2k+1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c005f474bffdcdc441dd48da631f605536c1fcf" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-3.171ex;width:13.798ex;height:7.509ex" alt="{\displaystyle 9!!\sum _{k=0}^{4}{\frac {1}{2k+1}}}"></span><sup id="cite_ref-379" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-379">[379]</a></sup></dd> <dd><b>1690</b> = number of compositions of 14 into powers of 2<sup id="cite_ref-380" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-380">[380]</a></sup></dd> <dd><b>1691</b> = the same upside down, which makes it a strobogrammatic number<sup id="cite_ref-381" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-381">[381]</a></sup></dd> <dd><b>1692</b> = coreful perfect number<sup id="cite_ref-382" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-382">[382]</a></sup></dd> <dd><b>1693</b> = smallest prime > 41<sup>2</sup>.<sup id="cite_ref-383" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-383">[383]</a></sup></dd> <dd><b>1694</b> = number of unimodular 2 × 2 matrices having all terms in {0,1,...,26}<sup id="cite_ref-384" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-384">[384]</a></sup></dd> <dd><b>1695</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Magic_constant" title="Magic constant">magic constant</a> of <i>n</i> × <i>n</i> normal <a target="_blank" href="https://en.wikipedia.org/wiki/Magic_square" title="Magic square">magic square</a> and <a target="_blank" href="https://en.wikipedia.org/wiki/Eight_queens_puzzle" title="Eight queens puzzle"><i>n</i>-queens problem</a> for <i>n</i> = 15. <a target="_blank" href="https://oeis.org/A000607" class="extiw" title="oeis:A000607">Number of partitions of 58 into prime parts</a></dd> <dd><b>1696</b> = sum of totient function for first 74 integers</dd> <dd><b>1697</b> = Friedlander-Iwaniec prime<sup id="cite_ref-385" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-385">[385]</a></sup></dd> <dd><b>1698</b> = number of rooted trees with 47 vertices in which vertices at the same level have the same degree<sup id="cite_ref-386" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-386">[386]</a></sup></dd> <dd><b>1699</b> = number of rooted trees with 48 vertices in which vertices at the same level have the same degree<sup id="cite_ref-387" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-387">[387]</a></sup></dd></dl> <h3><span class="mw-headline" id="1700_to_1799">1700 to 1799</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a target="_blank" href="https://en.wikipedia.org/w/index.php?title=1000_(number)&action=edit§ion=11" title="Edit section: 1700 to 1799">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <dl><dd><b>1700</b> = σ<sub>2</sub>(39): sum of squares of divisors of 39<sup id="cite_ref-388" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-388">[388]</a></sup></dd> <dd><b><a target="_blank" href="https://en.wikipedia.org/wiki/1701_(number)" title="1701 (number)">1701</a></b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind" title="Stirling numbers of the second kind"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\{{8 \atop 4}\right\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>{</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac linethickness="0"> <mn>8</mn> <mn>4</mn> </mfrac> </mrow> <mo>}</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\{{8 \atop 4}\right\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6f7a683e883eb133db8c904cbab23d8f20813bc" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-2.505ex;width:5.206ex;height:6.176ex" alt="{\displaystyle \left\{{8 \atop 4}\right\}}"></span></a>, decagonal number, hull number of the U.S.S. Enterprise on <i><a target="_blank" href="https://en.wikipedia.org/wiki/Star_Trek" title="Star Trek">Star Trek</a></i></dd> <dd><b>1702</b> = palindromic in 3 consecutive bases: 898<sub>14</sub>, 787<sub>15</sub>, 6A6<sub>16</sub></dd> <dd><b>1703</b> = 1703131131 / 1000077 and the divisors of 1703 are 1703, 131, 13 and 1<sup id="cite_ref-389" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-389">[389]</a></sup></dd> <dd><b>1704</b> = sum of the squares of the parts in the partitions of 18 into two distinct parts<sup id="cite_ref-390" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-390">[390]</a></sup></dd> <dd><b>1705</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Tribonacci_number" class="mw-redirect" title="Tribonacci number">tribonacci number</a><sup id="cite_ref-391" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-391">[391]</a></sup></dd> <dd><b>1706</b> = 1 + 4 + 16 + 64 + 256 + 1024 + 256 + 64 + 16 + 4 + 1 sum of fifth row of triangle of powers of 4<sup id="cite_ref-392" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-392">[392]</a></sup></dd> <dd><b>1707</b> = number of partitions of 30 in which the number of parts divides 30<sup id="cite_ref-393" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-393">[393]</a></sup></dd> <dd><b>1708</b> = 2<sup>2</sup> × 7 × 61 a number whose product of prime indices 1 × 1 × 4 × 18 is divisible by its sum of prime factors 2 + 2 + 7 + 61<sup id="cite_ref-394" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-394">[394]</a></sup></dd> <dd><b>1709</b> = first of a sequence of eight primes formed by adding <a target="_blank" href="https://en.wikipedia.org/wiki/57_(number)" title="57 (number)">57</a> in the middle. 1709, 175709, 17575709, 1757575709, 175757575709, 17575757575709, 1757575757575709 and 175757575757575709 are all prime, but 17575757575757575709 = 232433 × 75616446785773</dd> <dd><b>1710</b> = maximal number of pieces that can be obtained by cutting an annulus with 57 cuts<sup id="cite_ref-395" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-395">[395]</a></sup></dd> <dd><b>1711</b> = triangular number, <a target="_blank" href="https://en.wikipedia.org/wiki/Centered_decagonal_number" title="Centered decagonal number">centered decagonal number</a></dd> <dd><b>1712</b> = number of irredundant sets in the 29-cocktail party graph<sup id="cite_ref-396" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-396">[396]</a></sup></dd> <dd><b>1713</b> = number of aperiodic rooted trees with 12 nodes<sup id="cite_ref-397" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-397">[397]</a></sup></dd> <dd><b>1714</b> = number of regions formed by drawing the line segments connecting any two of the 18 perimeter points of an <a target="_blank" rel="nofollow" class="external text" href="https://oeis.org/A331452/a331452_20.png">3 × 6 grid of squares</a><sup id="cite_ref-398" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-398">[398]</a></sup></dd> <dd><b>1715</b> = k such that geometric mean of phi(k) and sigma(k) is an integer<sup id="cite_ref-399" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-399">[399]</a></sup></dd> <dd><b>1716</b> = 857 + 859: sum of twin prime pair<sup id="cite_ref-400" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-400">[400]</a></sup></dd> <dd><b>1717</b> = pentagonal number<sup id="cite_ref-Pentagonal_number_67-7" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pentagonal_number-67">[67]</a></sup></dd> <dd><b>1718</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{d|12}{\binom {12}{d}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mn>12</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mn>12</mn> <mi>d</mi> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{d|12}{\binom {12}{d}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22fefd4b9eea2ddd79b10c952adf48eabaac7c82" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-3.505ex;width:9.488ex;height:7.176ex" alt="{\displaystyle \sum _{d|12}{\binom {12}{d}}}"></span><sup id="cite_ref-401" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-401">[401]</a></sup></dd> <dd><b>1719</b> = composite <a target="_blank" href="https://en.wikipedia.org/wiki/De_Polignac_number" class="mw-redirect" title="De Polignac number">de Polignac number</a><sup id="cite_ref-402" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-402">[402]</a></sup></dd> <dd><b>1720</b> = sum of the first 31 primes</dd> <dd><b>1721</b> = number of squares between 42<sup>2</sup> and 42<sup>4</sup>.<sup id="cite_ref-403" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-403">[403]</a></sup></dd> <dd><b>1722</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Giuga_number" title="Giuga number">Giuga number</a>,<sup id="cite_ref-404" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-404">[404]</a></sup> pronic number<sup id="cite_ref-pronic_number_48-9" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-pronic_number-48">[48]</a></sup></dd> <dd><b>1723</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a></dd> <dd><b>1724</b> = maximal number of regions the plane is divided into by drawing 42 circles<sup id="cite_ref-405" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-405">[405]</a></sup></dd> <dd><b>1725</b> = 47<sup>2</sup> - 22<sup>2</sup> = (prime(15))<sup>2</sup> - (nonprime(15))<sup>2</sup><sup id="cite_ref-406" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-406">[406]</a></sup></dd> <dd><b>1726</b> = number of partitions of 44 into distinct and relatively prime parts<sup id="cite_ref-407" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-407">[407]</a></sup></dd> <dd><b>1727</b> = area of the 24th <a target="_blank" rel="nofollow" class="external text" href="https://oeis.org/A080663/a080663.jpg">conjoined trapezoid</a><sup id="cite_ref-408" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-408">[408]</a></sup></dd> <dd><b><a target="_blank" href="https://en.wikipedia.org/wiki/1728_(number)" title="1728 (number)">1728</a></b> = the quantity expressed as 1000 in <a target="_blank" href="https://en.wikipedia.org/wiki/Duodecimal" title="Duodecimal">duodecimal</a>, that is, the cube of <a target="_blank" href="https://en.wikipedia.org/wiki/12_(number)" title="12 (number)">twelve</a> (called a <a target="_blank" href="https://en.wikipedia.org/wiki/Great_gross" class="mw-redirect" title="Great gross">great gross</a>), and so, the number of cubic inches in a cubic <a target="_blank" href="https://en.wikipedia.org/wiki/Foot_(length)" class="mw-redirect" title="Foot (length)">foot</a>, palindromic in base 11 (1331<sub>11</sub>) and 23 (363<sub>23</sub>)</dd> <dd><b><a target="_blank" href="https://en.wikipedia.org/wiki/1729_(number)" title="1729 (number)">1729</a></b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Taxicab_number" title="Taxicab number">taxicab number</a>, Carmichael number, Zeisel number, centered cube number, <a target="_blank" href="https://en.wikipedia.org/wiki/Hardy%E2%80%93Ramanujan_number" class="mw-redirect" title="Hardy–Ramanujan number">Hardy–Ramanujan number</a>. In the decimal expansion of <a target="_blank" href="https://en.wikipedia.org/wiki/E_(mathematical_constant)" title="E (mathematical constant)">e</a> the first time all 10 digits appear in sequence starts at the 1729th digit (or 1728th decimal place). In 1979 the rock musical <i><a target="_blank" href="https://en.wikipedia.org/wiki/Hair_(musical)" title="Hair (musical)">Hair</a></i> closed on Broadway in New York City after 1729 performances. Palindromic in bases 12, 32, 36.</dd> <dd><b>1730</b> = 3 × 24<sup>2</sup> + 2 = number of points on surface of square pyramid of side-length 24<sup id="cite_ref-409" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-409">[409]</a></sup></dd> <dd><b>1731</b> = k such that geometric mean of phi(k) and sigma(k) is an integer<sup id="cite_ref-410" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-410">[410]</a></sup></dd> <dd><b>1732</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{k=0}^{5}{\binom {5}{k}}^{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </munderover> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mn>5</mn> <mi>k</mi> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=0}^{5}{\binom {5}{k}}^{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93474098500293918df771f309e6811a9c7f41ab" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-3.171ex;width:9.463ex;height:7.509ex" alt="{\displaystyle \sum _{k=0}^{5}{\binom {5}{k}}^{k}}"></span><sup id="cite_ref-411" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-411">[411]</a></sup></dd> <dd><b>1733</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Sophie_Germain_prime" class="mw-redirect" title="Sophie Germain prime">Sophie Germain prime</a>, palindromic in bases 3, 18, 19.</dd> <dd><b>1734</b> = surface area of a cube of edge length 17<sup id="cite_ref-412" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-412">[412]</a></sup></dd> <dd><b>1735</b> = number of partitions of 55 such that the smallest part is greater than or equal to number of parts<sup id="cite_ref-413" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-413">[413]</a></sup></dd> <dd><b>1736</b> = sum of totient function for first 75 integers, number of surface points on a cube with edge-length 18<sup id="cite_ref-A005897_16-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-A005897-16">[16]</a></sup></dd> <dd><b>1737</b> = pinwheel number<sup id="cite_ref-Pinwheel_87-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pinwheel-87">[87]</a></sup></dd> <dd><b>1738</b> = number of achiral integer partitions of 52<sup id="cite_ref-414" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-414">[414]</a></sup></dd> <dd><b>1739</b> = number of 1s in all partitions of 30 into odd parts<sup id="cite_ref-415" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-415">[415]</a></sup></dd> <dd><b>1740</b> = number of squares in the <a target="_blank" href="https://en.wikipedia.org/wiki/Aztec_diamond" title="Aztec diamond">Aztec diamond</a> of order 29<sup id="cite_ref-416" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-416">[416]</a></sup></dd> <dd><b>1741</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a>, centered square number<sup id="cite_ref-Centered_square_numbers_12-7" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_square_numbers-12">[12]</a></sup></dd> <dd><b>1742</b> = <a target="_blank" rel="nofollow" class="external text" href="https://mathworld.wolfram.com/PlaneDivisionbyEllipses.html">number of regions</a> the plane is divided into by 30 ellipses<sup id="cite_ref-417" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-417">[417]</a></sup></dd> <dd><b>1743</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Wiener_index" title="Wiener index">wiener index</a> of the <a target="_blank" href="https://en.wikipedia.org/wiki/Windmill_graph" title="Windmill graph">windmill graph</a> D(3,21)<sup id="cite_ref-418" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-418">[418]</a></sup></dd> <dd><b>1744</b> = k such that k, k+1 and k+2 are sums of 2 squares<sup id="cite_ref-419" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-419">[419]</a></sup></dd> <dd><b>1745</b> = 5-<a target="_blank" href="https://en.wikipedia.org/wiki/Kn%C3%B6del_number" title="Knödel number">Knödel number</a><sup id="cite_ref-420" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-420">[420]</a></sup></dd> <dd><b>1746</b> = number of unit-distance graphs on 8 nodes<sup id="cite_ref-421" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-421">[421]</a></sup></dd> <dd><b>1747</b> = balanced prime<sup id="cite_ref-Balanced_prime_88-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Balanced_prime-88">[88]</a></sup></dd> <dd><b>1748</b> = number of partitions of 55 into distinct parts in which the number of parts divides 55<sup id="cite_ref-422" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-422">[422]</a></sup></dd> <dd><b>1749</b> = number of integer partitions of 33 with no part dividing all the others<sup id="cite_ref-423" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-423">[423]</a></sup></dd> <dd><b>1750</b> = hypotenuse in three different Pythagorean triangles<sup id="cite_ref-424" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-424">[424]</a></sup></dd> <dd><b>1751</b> = <a target="_blank" rel="nofollow" class="external text" href="https://oeis.org/A144391/a144391.jpg">cropped hexagone</a><sup id="cite_ref-425" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-425">[425]</a></sup></dd> <dd><b>1752</b> = 79<sup>2</sup> - 67<sup>2</sup>, the only way to express 1752 as a difference of prime squares<sup id="cite_ref-426" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-426">[426]</a></sup></dd> <dd><b>1753</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Balanced_prime" title="Balanced prime">balanced prime</a><sup id="cite_ref-Balanced_prime_88-7" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Balanced_prime-88">[88]</a></sup></dd> <dd><b>1754</b> = k such that 5*2<sup>k</sup> - 1 is prime<sup id="cite_ref-427" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-427">[427]</a></sup></dd> <dd><b>1755</b> = number of integer partitions of 50 whose augmented differences are distinct<sup id="cite_ref-428" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-428">[428]</a></sup></dd> <dd><b>1756</b> = centered pentagonal number<sup id="cite_ref-Centered_pentagonal_43-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_pentagonal-43">[43]</a></sup></dd> <dd><b>1758</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{k=1}^{46}\sigma (k)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>46</mn> </mrow> </munderover> <mi>σ</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=1}^{46}\sigma (k)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5ad585aefd6e32335dc910c50c49c1d789cd30b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-3.005ex;width:8.092ex;height:7.343ex" alt="{\displaystyle \sum _{k=1}^{46}\sigma (k)}"></span><sup id="cite_ref-429" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-429">[429]</a></sup></dd> <dd><b>1759</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/De_Polignac_number" class="mw-redirect" title="De Polignac number">de Polignac</a> prime<sup id="cite_ref-430" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-430">[430]</a></sup></dd> <dd><b>1760</b> = the number of <a target="_blank" href="https://en.wikipedia.org/wiki/Yard" title="Yard">yards</a> in a mile</dd> <dd><b>1761</b> = k such that k, k+1 and k+2 are products of two primes<sup id="cite_ref-431" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-431">[431]</a></sup></dd> <dd><b>1762</b> = number of binary sequences of length 12 and <a target="_blank" rel="nofollow" class="external text" href="http://neilsloane.com/doc/CNC.pdf">curling number 2</a><sup id="cite_ref-432" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-432">[432]</a></sup></dd> <dd><b>1763</b> = number of edges in the join of two cycle graphs, both of order 41<sup id="cite_ref-433" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-433">[433]</a></sup></dd> <dd><b>1764</b> = 42<sup>2</sup></dd> <dd><b>1765</b> = number of stacks, or planar partitions of 15<sup id="cite_ref-434" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-434">[434]</a></sup></dd> <dd><b>1766</b> = number of points on surface of octahedron with edgelength 21<sup id="cite_ref-435" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-435">[435]</a></sup></dd> <dd><b>1767</b> = σ(28<sup>2</sup>) = σ(35<sup>2</sup>)<sup id="cite_ref-436" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-436">[436]</a></sup></dd> <dd><b>1768</b> = number of nonequivalent dissections of an hendecagon into 8 polygons by nonintersecting diagonals up to rotation<sup id="cite_ref-437" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-437">[437]</a></sup></dd> <dd><b>1769</b> = maximal number of pieces that can be obtained by cutting an annulus with 58 cuts<sup id="cite_ref-438" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-438">[438]</a></sup></dd> <dd><b>1770</b> = triangular number, hexagonal number,<sup id="cite_ref-Hexagonal_number_26-7" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Hexagonal_number-26">[26]</a></sup> <a target="_blank" href="https://en.wikipedia.org/wiki/Seventeen_Seventy,_Queensland" title="Seventeen Seventy, Queensland">Seventeen Seventy</a>, town in Australia</dd> <dd><b>1771</b> = tetrahedral number<sup id="cite_ref-Leyland_number_105-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Leyland_number-105">[105]</a></sup></dd> <dd><b>1772</b> = centered heptagonal number,<sup id="cite_ref-centered_heptagonal_number_63-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-centered_heptagonal_number-63">[63]</a></sup> sum of totient function for first 76 integers</dd> <dd><b>1773</b> = number of words of length 5 over the alphabet {1,2,3,4,5} such that no two even numbers appear consecutively<sup id="cite_ref-439" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-439">[439]</a></sup></dd> <dd><b>1774</b> = number of rooted identity trees with 15 nodes and 5 leaves<sup id="cite_ref-440" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-440">[440]</a></sup></dd> <dd><b>1775</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{1\leq i\leq 10}prime(i)\cdot (2\cdot i-1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>≤</mo> <mi>i</mi> <mo>≤</mo> <mn>10</mn> </mrow> </munder> <mi>p</mi> <mi>r</mi> <mi>i</mi> <mi>m</mi> <mi>e</mi> <mo stretchy="false">(</mo> <mi>i</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>⋅</mo> <mi>i</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{1\leq i\leq 10}prime(i)\cdot (2\cdot i-1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/306ffd8b89956353c8e836638a6e9f30a359995a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-3.171ex;width:25.869ex;height:5.676ex" alt="{\displaystyle \sum _{1\leq i\leq 10}prime(i)\cdot (2\cdot i-1)}"></span>: sum of piles of first 10 primes<sup id="cite_ref-441" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-441">[441]</a></sup></dd> <dd><b>1776</b> = <a target="_blank" rel="nofollow" class="external text" href="https://oeis.org/A045944/a045944_1.jpg">square star number</a><sup id="cite_ref-442" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-442">[442]</a></sup></dd> <dd><b>1777</b> = smallest prime > 42<sup>2</sup>.<sup id="cite_ref-443" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-443">[443]</a></sup></dd> <dd><b>1778</b> = least k >= 1 such that the remainder when 6<sup>k</sup> is divided by k is 22<sup id="cite_ref-444" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-444">[444]</a></sup></dd> <dd><b>1779</b> = number of achiral integer partitions of 53<sup id="cite_ref-445" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-445">[445]</a></sup></dd> <dd><b>1780</b> = number of lattice paths from (0, 0) to (7, 7) using E (1, 0) and N (0, 1) as steps that horizontally cross the diagonal y = x with even many times<sup id="cite_ref-446" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-446">[446]</a></sup></dd> <dd><b>1781</b> = the first 1781 digits of e form a prime<sup id="cite_ref-447" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-447">[447]</a></sup></dd> <dd><b>1782</b> = heptagonal number<sup id="cite_ref-heptagonal_number_62-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-heptagonal_number-62">[62]</a></sup></dd> <dd><b>1783</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/De_Polignac_number" class="mw-redirect" title="De Polignac number">de Polignac</a> prime<sup id="cite_ref-448" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-448">[448]</a></sup></dd> <dd><b>1784</b> = number of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} such that every pair of distinct elements has a different quotient<sup id="cite_ref-449" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-449">[449]</a></sup></dd> <dd><b>1785</b> = square pyramidal number,<sup id="cite_ref-Square_pyramidal_numbers_14-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Square_pyramidal_numbers-14">[14]</a></sup> triangular matchstick number<sup id="cite_ref-auto5_45-8" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-auto5-45">[45]</a></sup></dd> <dd><b>1786</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Centered_triangular_number" title="Centered triangular number">centered triangular number</a><sup id="cite_ref-450" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-450">[450]</a></sup></dd> <dd><b>1787</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a>, sum of eleven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191)</dd> <dd><b>1788</b> = Euler transform of -1, -2, ..., -34<sup id="cite_ref-451" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-451">[451]</a></sup></dd> <dd><b>1789</b> = number of wiggly sums adding to 17 (terms alternately increase and decrease or vice versa)<sup id="cite_ref-452" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-452">[452]</a></sup></dd> <dd><b>1790</b> = number of partitions of 50 into pairwise relatively prime parts<sup id="cite_ref-453" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-453">[453]</a></sup></dd> <dd><b>1791</b> = largest natural number that cannot be expressed as a sum of at most four <a target="_blank" href="https://en.wikipedia.org/wiki/Hexagonal_number" title="Hexagonal number">hexagonal numbers</a>.</dd> <dd><b>1792</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Granville_number" title="Granville number">Granville number</a></dd> <dd><b>1793</b> = number of lattice points inside a circle of radius 24<sup id="cite_ref-454" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-454">[454]</a></sup></dd> <dd><b>1794</b> = nonagonal number,<sup id="cite_ref-Nonagonal_number_151-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Nonagonal_number-151">[151]</a></sup> number of partitions of 33 that do not contain 1 as a part<sup id="cite_ref-auto8_31-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-auto8-31">[31]</a></sup></dd> <dd><b>1795</b> = number of heptagons with perimeter 38<sup id="cite_ref-455" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-455">[455]</a></sup></dd> <dd><b>1796</b> = k such that geometric mean of phi(k) and sigma(k) is an integer<sup id="cite_ref-456" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-456">[456]</a></sup></dd> <dd><b>1797</b> = number k such that phi(prime(k)) is a square<sup id="cite_ref-457" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-457">[457]</a></sup></dd> <dd><b>1798</b> = 2 × 29 × 31 = 10<sub>2</sub> × 11101<sub>2</sub> × 11111<sub>2</sub>, which yield zero when the prime factors are xored together<sup id="cite_ref-458" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-458">[458]</a></sup></dd> <dd><b>1799</b> = 2 × 30<sup>2</sup> − 1 = a <a target="_blank" rel="nofollow" class="external text" href="https://oeis.org/A056220/a056220.jpg">twin square</a><sup id="cite_ref-459" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-459">[459]</a></sup></dd></dl> <h3><span class="mw-headline" id="1800_to_1899">1800 to 1899</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a target="_blank" href="https://en.wikipedia.org/w/index.php?title=1000_(number)&action=edit§ion=12" title="Edit section: 1800 to 1899">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <dl><dd><b>1800</b> = pentagonal pyramidal number,<sup id="cite_ref-Pentagonal_pyramidal_number_268-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pentagonal_pyramidal_number-268">[268]</a></sup> <a target="_blank" href="https://en.wikipedia.org/wiki/Achilles_number" title="Achilles number">Achilles number</a>, also, in da Ponte's <i><a target="_blank" href="https://en.wikipedia.org/wiki/Don_Giovanni" title="Don Giovanni">Don Giovanni</a></i>, the number of women Don Giovanni had slept with so far when confronted by Donna Elvira, according to Leporello's tally</dd> <dd><b>1801</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Cuban_prime" title="Cuban prime">cuban prime</a>, sum of five and nine consecutive primes (349 + 353 + 359 + 367 + 373 and 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227)<sup id="cite_ref-Cuban_Prime_352-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Cuban_Prime-352">[352]</a></sup></dd> <dd><b>1802</b> = 2 × 30<sup>2</sup> + 2 = number of points on surface of tetrahedron with edgelength 30,<sup id="cite_ref-460" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-460">[460]</a></sup> number of partitions of 30 such that the number of odd parts is a part<sup id="cite_ref-461" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-461">[461]</a></sup></dd> <dd><b>1803</b> = number of <a target="_blank" href="https://en.wikipedia.org/wiki/Polyhex_(mathematics)" title="Polyhex (mathematics)">decahexes</a> that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion)<sup id="cite_ref-462" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-462">[462]</a></sup></dd> <dd><b>1804</b> = <a target="_blank" href="https://oeis.org/A006316" class="extiw" title="oeis:A006316">number k such that k^64 + 1 is prime</a></dd> <dd><b>1805</b> = number of squares between 43<sup>2</sup> and 43<sup>4</sup>.<sup id="cite_ref-463" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-463">[463]</a></sup></dd> <dd><b>1806</b> = pronic number,<sup id="cite_ref-pronic_number_48-10" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-pronic_number-48">[48]</a></sup> product of first four terms of <a target="_blank" href="https://en.wikipedia.org/wiki/Sylvester%27s_sequence" title="Sylvester's sequence">Sylvester's sequence</a>, <a target="_blank" href="https://en.wikipedia.org/wiki/Primary_pseudoperfect_number" title="Primary pseudoperfect number">primary pseudoperfect number</a>,<sup id="cite_ref-464" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-464">[464]</a></sup> only number for which <i>n</i> equals the denominator of the <i>n</i>th <a target="_blank" href="https://en.wikipedia.org/wiki/Bernoulli_number" title="Bernoulli number">Bernoulli number</a>,<sup id="cite_ref-465" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-465">[465]</a></sup> <a target="_blank" href="https://en.wikipedia.org/wiki/Schr%C3%B6der_number" title="Schröder number">Schröder number</a><sup id="cite_ref-466" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-466">[466]</a></sup></dd> <dd><b>1807</b> = fifth term of Sylvester's sequence<sup id="cite_ref-467" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-467">[467]</a></sup></dd> <dd><b>1808</b> = maximal number of regions the plane is divided into by drawing 43 circles<sup id="cite_ref-468" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-468">[468]</a></sup></dd> <dd><b>1809</b> = sum of first 17 <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-primes</a><sup id="cite_ref-469" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-469">[469]</a></sup></dd> <dd><b>1810</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{k=0}^{4}{\binom {4}{k}}^{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </munderover> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mrow class="MJX-TeXAtom-OPEN"> <mo maxsize="2.047em" minsize="2.047em">(</mo> </mrow> <mfrac linethickness="0"> <mn>4</mn> <mi>k</mi> </mfrac> <mrow class="MJX-TeXAtom-CLOSE"> <mo maxsize="2.047em" minsize="2.047em">)</mo> </mrow> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=0}^{4}{\binom {4}{k}}^{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/015f68e346530a1eb56137649bf0d0f951a2e529" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-3.171ex;width:9.429ex;height:7.509ex" alt="{\displaystyle \sum _{k=0}^{4}{\binom {4}{k}}^{4}}"></span><sup id="cite_ref-470" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-470">[470]</a></sup></dd> <dd><b>1811</b> = Sophie Germain prime</dd> <dd><b>1812</b> = n such that n<sup>32</sup> + 1 is prime<sup id="cite_ref-471" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-471">[471]</a></sup></dd> <dd><b>1813</b> = number of <a target="_blank" href="https://en.wikipedia.org/wiki/Polyominoes" class="mw-redirect" title="Polyominoes">polyominoes</a> with 26 cells, symmetric about two orthogonal axes<sup id="cite_ref-472" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-472">[472]</a></sup></dd> <dd><b>1814</b> = 1 + 6 + 36 + 216 + 1296 + 216 + 36 + 6 + 1 = sum of 4th row of triangle of powers of six<sup id="cite_ref-473" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-473">[473]</a></sup></dd> <dd><b>1815</b> = polygonal chain number <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \#(P_{2,1}^{3})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">#</mi> <mo stretchy="false">(</mo> <msubsup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msubsup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \#(P_{2,1}^{3})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7e2e900d7f9bf2e309486a7be4a7234c36704f5" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-1.338ex;width:7.571ex;height:3.509ex" alt="{\displaystyle \#(P_{2,1}^{3})}"></span><sup id="cite_ref-474" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-474">[474]</a></sup></dd> <dd><b>1816</b> = number of strict partions of 44<sup id="cite_ref-475" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-475">[475]</a></sup></dd> <dd><b>1817</b> = total number of prime parts in all partitions of 20<sup id="cite_ref-476" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-476">[476]</a></sup></dd> <dd><b>1818</b> = n such that n<sup>32</sup> + 1 is prime<sup id="cite_ref-477" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-477">[477]</a></sup></dd> <dd><b>1819</b> = sum of the first 32 primes, minus 32<sup id="cite_ref-478" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-478">[478]</a></sup></dd> <dd><b>1820</b> = pentagonal number,<sup id="cite_ref-Pentagonal_number_67-8" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pentagonal_number-67">[67]</a></sup> pentatope number,<sup id="cite_ref-Pentatope_number_217-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pentatope_number-217">[217]</a></sup> number of compositions of 13 whose run-lengths are either weakly increasing or weakly decreasing<sup id="cite_ref-auto1_479-0" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-auto1-479">[479]</a></sup></dd> <dd><b>1821</b> = member of the Mian–Chowla sequence<sup id="cite_ref-Mian-Chowla_15-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Mian-Chowla-15">[15]</a></sup></dd> <dd><b>1822</b> = number of integer partitions of 43 whose distinct parts are connected<sup id="cite_ref-480" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-480">[480]</a></sup></dd> <dd><b>1823</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a>, safe prime<sup id="cite_ref-Safe_primes_19-10" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Safe_primes-19">[19]</a></sup></dd> <dd><b>1824</b> = 43<sup>2</sup> - 5<sup>2</sup>, the only way to express 1824 as a difference of prime squares<sup id="cite_ref-481" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-481">[481]</a></sup></dd> <dd><b>1825</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Octagonal_number" title="Octagonal number">octagonal number</a><sup id="cite_ref-482" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-482">[482]</a></sup></dd> <dd><b>1826</b> = decagonal pyramidal number<sup id="cite_ref-483" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-483">[483]</a></sup></dd> <dd><b>1827</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Vampire_number" title="Vampire number">vampire number</a><sup id="cite_ref-Vampire_number_171-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Vampire_number-171">[171]</a></sup></dd> <dd><b>1828</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Meandric_number" class="mw-redirect" title="Meandric number">meandric number</a>, <a target="_blank" href="https://en.wikipedia.org/wiki/Open_meandric_number" class="mw-redirect" title="Open meandric number">open meandric number</a>, <a target="_blank" href="https://en.wikipedia.org/wiki/Mathematical_coincidence" title="Mathematical coincidence">appears twice</a> in the first 10 decimal digits of <i><a target="_blank" href="https://en.wikipedia.org/wiki/E_(mathematical_constant)" title="E (mathematical constant)">e</a></i></dd> <dd><b>1829</b> = composite <a target="_blank" href="https://en.wikipedia.org/wiki/De_Polignac_number" class="mw-redirect" title="De Polignac number">de Polignac number</a><sup id="cite_ref-484" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-484">[484]</a></sup></dd> <dd><b>1830</b> = triangular number</dd> <dd><b>1831</b> = smallest prime with a gap of exactly 16 to next prime (1847)<sup id="cite_ref-485" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-485">[485]</a></sup></dd> <dd><b>1832</b> = sum of totient function for first 77 integers</dd> <dd><b>1833</b> = number of atoms in a decahedron with 13 shells<sup id="cite_ref-486" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-486">[486]</a></sup></dd> <dd><b>1834</b> = octahedral number,<sup id="cite_ref-Octahedral_number_124-2" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Octahedral_number-124">[124]</a></sup> sum of the cubes of the first five primes</dd> <dd><b>1835</b> = absolute value of numerator of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{6}^{(5)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>5</mn> <mo stretchy="false">)</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{6}^{(5)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7203cc1616186012ea7706eaa5c59108afa57ac5" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-1.005ex;width:4.258ex;height:3.676ex" alt="{\displaystyle D_{6}^{(5)}}"></span><sup id="cite_ref-487" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-487">[487]</a></sup></dd> <dd><b>1836</b> = factor by which a <a target="_blank" href="https://en.wikipedia.org/wiki/Proton" title="Proton">proton</a> is more massive than an <a target="_blank" href="https://en.wikipedia.org/wiki/Electron" title="Electron">electron</a></dd> <dd><b>1837</b> = star number<sup id="cite_ref-Centered_12-gonal_numbers_80-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_12-gonal_numbers-80">[80]</a></sup></dd> <dd><b>1838</b> = number of unimodular 2 × 2 matrices having all terms in {0,1,...,27}<sup id="cite_ref-488" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-488">[488]</a></sup></dd> <dd><b>1839</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lfloor {\sqrt[{3}]{13!}}\rfloor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⌊</mo> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mrow> <mn>13</mn> <mo>!</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </mroot> </mrow> <mo fence="false" stretchy="false">⌋</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lfloor {\sqrt[{3}]{13!}}\rfloor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f0943f39851d7f678812a33ee092226567c63e4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-0.838ex;width:6.972ex;height:3.176ex" alt="{\displaystyle \lfloor {\sqrt[{3}]{13!}}\rfloor }"></span><sup id="cite_ref-489" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-489">[489]</a></sup></dd> <dd><b>1840</b> = 43<sup>2</sup> - 3<sup>2</sup>, the only way to express 1840 as a difference of prime squares<sup id="cite_ref-490" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-490">[490]</a></sup></dd> <dd><b>1841</b> = Mertens function zero</dd> <dd><b>1842</b> = number of unlabeled rooted trees with 11 nodes<sup id="cite_ref-491" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-491">[491]</a></sup></dd> <dd><b>1843</b> = Mertens function zero</dd> <dd><b>1844</b> = Mertens function zero</dd> <dd><b>1845</b> = Mertens function zero</dd> <dd><b>1846</b> = sum of first 49 composite numbers<sup id="cite_ref-492" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-492">[492]</a></sup></dd> <dd><b>1847</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a></dd> <dd><b>1848</b> = number of edges in the join of two cycle graphs, both of order 42<sup id="cite_ref-493" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-493">[493]</a></sup></dd> <dd><b>1849</b> = 43<sup>2</sup>, palindromic in base 6 (= 12321<sub>6</sub>), centered octagonal number<sup id="cite_ref-Centered_octagonal_number_156-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_octagonal_number-156">[156]</a></sup></dd> <dd><b>1850</b> = <a target="_blank" href="https://oeis.org/A000607" class="extiw" title="oeis:A000607">Number of partitions of 59 into prime parts</a></dd> <dd><b>1851</b> = sum of the first 32 primes</dd> <dd><b>1852</b> = number of quantales on 5 elements, up to isomorphism<sup id="cite_ref-494" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-494">[494]</a></sup></dd> <dd><b>1853</b> = Mertens function zero</dd> <dd><b>1854</b> = Mertens function zero</dd> <dd><b>1855</b> = rencontres number: number of permutations of [7] with exactly one fixed point<sup id="cite_ref-495" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-495">[495]</a></sup></dd> <dd><b>1856</b> = sum of totient function for first 78 integers</dd> <dd><b>1857</b> = Mertens function zero, pinwheel number<sup id="cite_ref-Pinwheel_87-7" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pinwheel-87">[87]</a></sup></dd> <dd><b>1858</b> = number of 14-carbon alkanes C<sub>14</sub>H<sub>30</sub> ignoring stereoisomers<sup id="cite_ref-496" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-496">[496]</a></sup></dd> <dd><b>1859</b> = composite <a target="_blank" href="https://en.wikipedia.org/wiki/De_Polignac_number" class="mw-redirect" title="De Polignac number">de Polignac number</a><sup id="cite_ref-497" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-497">[497]</a></sup></dd> <dd><b>1860</b> = number of squares in the <a target="_blank" href="https://en.wikipedia.org/wiki/Aztec_diamond" title="Aztec diamond">Aztec diamond</a> of order 30<sup id="cite_ref-498" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-498">[498]</a></sup></dd> <dd><b>1861</b> = centered square number,<sup id="cite_ref-Centered_square_numbers_12-8" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_square_numbers-12">[12]</a></sup> Mertens function zero</dd> <dd><b>1862</b> = Mertens function zero, forms a Ruth–Aaron pair with 1863 under second definition</dd> <dd><b>1863</b> = Mertens function zero, forms a Ruth–Aaron pair with 1862 under second definition</dd> <dd><b>1864</b> = Mertens function zero, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1864!-2}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1864</mn> <mo>!</mo> <mo>−</mo> <mn>2</mn> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1864!-2}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/647a7cf163303fb64a7323369944c12c96af4b03" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-1.838ex;width:10.136ex;height:5.343ex" alt="{\displaystyle {\frac {1864!-2}{2}}}"></span> is a prime<sup id="cite_ref-499" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-499">[499]</a></sup></dd> <dd><b>1865</b> = 12345<sub>6</sub>: Largest <a target="_blank" href="https://en.wikipedia.org/wiki/Senary" title="Senary">senary</a> metadrome (number with digits in strict ascending order in base 6)<sup id="cite_ref-500" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-500">[500]</a></sup></dd> <dd><b>1866</b> = Mertens function zero, number of plane partitions of 16 with at most two rows<sup id="cite_ref-501" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-501">[501]</a></sup></dd> <dd><b>1867</b> = prime <a target="_blank" href="https://en.wikipedia.org/wiki/De_Polignac_number" class="mw-redirect" title="De Polignac number">de Polignac number</a><sup id="cite_ref-502" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-502">[502]</a></sup></dd> <dd><b>1868</b> = smallest number of complexity 21: smallest number requiring 21 1's to build using +, * and ^<sup id="cite_ref-503" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-503">[503]</a></sup></dd> <dd><b>1869</b> = Hultman number: S<sub>H</sub>(7, 4)<sup id="cite_ref-504" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-504">[504]</a></sup></dd> <dd><b>1870</b> = decagonal number<sup id="cite_ref-Decagonal_91-4" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Decagonal-91">[91]</a></sup></dd> <dd><b>1871</b> = the first prime of the 2 consecutive twin prime pairs: (1871, 1873) and (1877, 1879)<sup id="cite_ref-505" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-505">[505]</a></sup></dd> <dd><b>1872</b> = first Zagreb index of the complete graph K<sub>13</sub><sup id="cite_ref-506" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-506">[506]</a></sup></dd> <dd><b>1873</b> = number of Narayana's cows and calves after 21 years<sup id="cite_ref-507" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-507">[507]</a></sup></dd> <dd><b>1874</b> = area of the 25th <a target="_blank" rel="nofollow" class="external text" href="https://oeis.org/A080663/a080663.jpg">conjoined trapezoid</a><sup id="cite_ref-508" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-508">[508]</a></sup></dd> <dd><b>1875</b> = 50<sup>2</sup> - 25<sup>2</sup></dd> <dd><b>1876</b> = <a target="_blank" href="https://oeis.org/A006316" class="extiw" title="oeis:A006316">number k such that k^64 + 1 is prime</a></dd> <dd><b>1877</b> = number of partitions of 39 where 39 divides the product of the parts<sup id="cite_ref-509" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-509">[509]</a></sup></dd> <dd><b>1878</b> = n such that n<sup>32</sup> + 1 is prime<sup id="cite_ref-510" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-510">[510]</a></sup></dd> <dd><b>1879</b> = a prime with square index<sup id="cite_ref-511" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-511">[511]</a></sup></dd> <dd><b>1880</b> = the 10th element of the self convolution of <a target="_blank" href="https://en.wikipedia.org/wiki/Lucas_numbers" class="mw-redirect" title="Lucas numbers">Lucas numbers</a><sup id="cite_ref-512" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-512">[512]</a></sup></dd> <dd><b>1881</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Triaugmented_triangular_prism" title="Triaugmented triangular prism">tricapped prism</a> number<sup id="cite_ref-513" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-513">[513]</a></sup></dd> <dd><b>1882</b> = number of <a target="_blank" href="https://en.wikipedia.org/wiki/Linear_separability" title="Linear separability">linearly separable</a> <a target="_blank" href="https://en.wikipedia.org/wiki/Boolean_functions" class="mw-redirect" title="Boolean functions">boolean functions</a> in 4 variables<sup id="cite_ref-514" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-514">[514]</a></sup></dd> <dd><b>1883</b> = number of conjugacy classes in the alternating group A<sub>28</sub><sup id="cite_ref-515" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-515">[515]</a></sup></dd> <dd><b>1884</b> = k such that 5*2<sup>k</sup> - 1 is prime<sup id="cite_ref-516" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-516">[516]</a></sup></dd> <dd><b>1885</b> = Zeisel number<sup id="cite_ref-Zeisel_number_244-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Zeisel_number-244">[244]</a></sup></dd> <dd><b>1886</b> = number of partitions of 6<sup>4</sup> into fourth powers<sup id="cite_ref-517" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-517">[517]</a></sup></dd> <dd><b>1887</b> = number of edges in the <a target="_blank" href="https://en.wikipedia.org/wiki/File:Hexagonal_triangle.png" title="File:Hexagonal triangle.png">hexagonal triangle</a> T(34)<sup id="cite_ref-518" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-518">[518]</a></sup></dd> <dd><b>1888</b> = primitive abundant number (<a target="_blank" href="https://en.wikipedia.org/wiki/Abundant_number" title="Abundant number">abundant number</a> all of whose proper divisors are <a target="_blank" href="https://en.wikipedia.org/wiki/Deficient_numbers" class="mw-redirect" title="Deficient numbers">deficient numbers</a>)<sup id="cite_ref-519" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-519">[519]</a></sup></dd> <dd><b>1889</b> = Sophie Germain prime, highly cototient number<sup id="cite_ref-highly_cototient_40-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-highly_cototient-40">[40]</a></sup></dd> <dd><b>1890</b> = triangular matchstick number<sup id="cite_ref-auto5_45-9" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-auto5-45">[45]</a></sup></dd> <dd><b>1891</b> = triangular number, hexagonal number,<sup id="cite_ref-Hexagonal_number_26-8" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Hexagonal_number-26">[26]</a></sup> centered pentagonal number,<sup id="cite_ref-Centered_pentagonal_43-7" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_pentagonal-43">[43]</a></sup> <a target="_blank" href="https://en.wikipedia.org/wiki/Centered_triangular_number" title="Centered triangular number">centered triangular number</a><sup id="cite_ref-520" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-520">[520]</a></sup></dd> <dd><b>1892</b> = pronic number<sup id="cite_ref-pronic_number_48-11" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-pronic_number-48">[48]</a></sup></dd> <dd><b>1893</b> = 44<sup>2</sup> - 44 + 1 = H<sub>44</sub> (the 44th Hogben number)<sup id="cite_ref-521" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-521">[521]</a></sup></dd> <dd><b>1894</b> = maximal number of regions the plane is divided into by drawing 44 circles<sup id="cite_ref-522" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-522">[522]</a></sup></dd> <dd><b>1895</b> = Stern-Jacobsthal number<sup id="cite_ref-523" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-523">[523]</a></sup></dd> <dd><b>1896</b> = member of the Mian-Chowla sequence<sup id="cite_ref-Mian-Chowla_15-7" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Mian-Chowla-15">[15]</a></sup></dd> <dd><b>1897</b> = member of Padovan sequence,<sup id="cite_ref-Padovan_sequence_68-2" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Padovan_sequence-68">[68]</a></sup> number of triangle-free graphs on 9 vertices<sup id="cite_ref-524" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-524">[524]</a></sup></dd> <dd><b>1898</b> = smallest multiple of n whose digits sum to 26<sup id="cite_ref-525" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-525">[525]</a></sup></dd> <dd><b>1899</b> = <a target="_blank" rel="nofollow" class="external text" href="https://oeis.org/A144391/a144391.jpg">cropped hexagone</a><sup id="cite_ref-526" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-526">[526]</a></sup></dd></dl> <h3><span class="mw-headline" id="1900_to_1999">1900 to 1999</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a target="_blank" href="https://en.wikipedia.org/w/index.php?title=1000_(number)&action=edit§ion=13" title="Edit section: 1900 to 1999">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <dl><dd><b>1900</b> = number of primes <= 2<sup>14</sup>.<sup id="cite_ref-auto3_22-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-auto3-22">[22]</a></sup> Also <a target="_blank" href="https://en.wikipedia.org/wiki/1900_(film)" title="1900 (film)"><i>1900</i> (film)</a> or <i>Novecento</i>, 1976 movie</dd> <dd><b>1901</b> = Sophie Germain prime, <a target="_blank" href="https://en.wikipedia.org/wiki/Centered_decagonal_number" title="Centered decagonal number">centered decagonal number</a></dd> <dd><b>1902</b> = number of symmetric plane partitions of 27<sup id="cite_ref-527" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-527">[527]</a></sup></dd> <dd><b>1903</b> = generalized catalan number<sup id="cite_ref-528" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-528">[528]</a></sup></dd> <dd><b>1904</b> = number of flat partitions of 43<sup id="cite_ref-529" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-529">[529]</a></sup></dd> <dd><b>1905</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Fermat_pseudoprime" title="Fermat pseudoprime">Fermat pseudoprime</a><sup id="cite_ref-530" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-530">[530]</a></sup></dd> <dd><b>1906</b> = number n such that 3<sup>n</sup> - 8 is prime<sup id="cite_ref-531" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-531">[531]</a></sup></dd> <dd><b>1907</b> = safe prime,<sup id="cite_ref-Safe_primes_19-11" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Safe_primes-19">[19]</a></sup> balanced prime<sup id="cite_ref-Balanced_prime_88-8" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Balanced_prime-88">[88]</a></sup></dd> <dd><b>1908</b> = coreful perfect number<sup id="cite_ref-532" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-532">[532]</a></sup></dd> <dd><b>1909</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Hyperperfect_number" title="Hyperperfect number">hyperperfect number</a><sup id="cite_ref-533" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-533">[533]</a></sup></dd> <dd><b>1910</b> = number of compositions of 13 having exactly one fixed point<sup id="cite_ref-534" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-534">[534]</a></sup></dd> <dd><b>1911</b> = heptagonal pyramidal number<sup id="cite_ref-535" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-535">[535]</a></sup></dd> <dd><b>1912</b> = size of 6th maximum raising after one blind in pot-limit poker<sup id="cite_ref-536" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-536">[536]</a></sup></dd> <dd><b>1913</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Super-prime" title="Super-prime">super-prime</a>, Honaker prime<sup id="cite_ref-537" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-537">[537]</a></sup></dd> <dd><b>1914</b> = number of bipartite partitions of 12 white objects and 3 black ones<sup id="cite_ref-538" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-538">[538]</a></sup></dd> <dd><b>1915</b> = number of nonisomorphic semigroups of order 5<sup id="cite_ref-539" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-539">[539]</a></sup></dd> <dd><b>1916</b> = sum of first 50 composite numbers<sup id="cite_ref-540" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-540">[540]</a></sup></dd> <dd><b>1917</b> = number of partitions of 51 into pairwise relatively prime parts<sup id="cite_ref-541" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-541">[541]</a></sup></dd> <dd><b>1918</b> = heptagonal number<sup id="cite_ref-heptagonal_number_62-7" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-heptagonal_number-62">[62]</a></sup></dd> <dd><b>1919</b> = smallest number with reciprocal of period length 36 in base 10<sup id="cite_ref-542" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-542">[542]</a></sup></dd> <dd><b>1920</b> = <a target="_blank" href="https://oeis.org/A006002" class="extiw" title="oeis:A006002">sum of the nontriangular numbers between successive triangular numbers</a></dd> <dd><b>1921</b> = 4-dimensional centered cube number<sup id="cite_ref-543" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-543">[543]</a></sup></dd> <dd><b>1922</b> = Area of a square with diagonal 62<sup id="cite_ref-area_of_a_square_with_diagonal_2n_51-3" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-area_of_a_square_with_diagonal_2n-51">[51]</a></sup></dd> <dd><b>1923</b> = 2 × 31<sup>2</sup> + 1 = number of different 2 X 2 determinants with integer entries from 0 to 31<sup id="cite_ref-544" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-544">[544]</a></sup></dd> <dd><b>1924</b> = 2 × 31<sup>2</sup> + 2 = number of points on surface of tetrahedron with edgelength 31<sup id="cite_ref-545" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-545">[545]</a></sup></dd> <dd><b>1925</b> = number of ways to write 24 as an orderless product of orderless sums<sup id="cite_ref-546" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-546">[546]</a></sup></dd> <dd><b>1926</b> = pentagonal number<sup id="cite_ref-Pentagonal_number_67-9" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pentagonal_number-67">[67]</a></sup></dd> <dd><b>1927</b> = 2<sup>11</sup> - 11<sup>2</sup><sup id="cite_ref-547" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-547">[547]</a></sup></dd> <dd><b>1928</b> = number of distinct values taken by 2^2^...^2 (with 13 2's and parentheses inserted in all possible ways)<sup id="cite_ref-548" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-548">[548]</a></sup></dd> <dd><b>1929</b> = Mertens function zero, number of integer partitions of 42 whose distinct parts are connected<sup id="cite_ref-549" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-549">[549]</a></sup></dd> <dd><b>1930</b> = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 53<sup id="cite_ref-550" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-550">[550]</a></sup></dd> <dd><b>1931</b> = Sophie Germain prime</dd> <dd><b>1932</b> = number of partitions of 40 into prime power parts<sup id="cite_ref-551" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-551">[551]</a></sup></dd> <dd><b>1933</b> = centered heptagonal number,<sup id="cite_ref-centered_heptagonal_number_63-6" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-centered_heptagonal_number-63">[63]</a></sup> Honaker prime<sup id="cite_ref-552" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-552">[552]</a></sup></dd> <dd><b>1934</b> = sum of totient function for first 79 integers</dd> <dd><b>1935</b> = number of edges in the join of two cycle graphs, both of order 43<sup id="cite_ref-553" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-553">[553]</a></sup></dd> <dd><b>1936</b> = 44<sup>2</sup>, 18-gonal number,<sup id="cite_ref-554" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-554">[554]</a></sup> 324-gonal number.</dd> <dd><b>1937</b> = number of chiral n-ominoes in 12-space, one cell labeled<sup id="cite_ref-555" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-555">[555]</a></sup></dd> <dd><b>1938</b> = Mertens function zero, number of points on surface of octahedron with edgelength 22<sup id="cite_ref-556" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-556">[556]</a></sup></dd> <dd><b>1939</b> = 7-Knödel number<sup id="cite_ref-557" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-557">[557]</a></sup></dd> <dd><b>1940</b> = the Mahonian number: T(8, 9)<sup id="cite_ref-A008302_157-2" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-A008302-157">[157]</a></sup></dd> <dd><b>1941</b> = maximal number of regions obtained by joining 16 points around a circle by straight lines<sup id="cite_ref-558" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-558">[558]</a></sup></dd> <dd><b>1942</b> = number k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes<sup id="cite_ref-559" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-559">[559]</a></sup></dd> <dd><b>1943</b> = largest number not the sum of distinct tetradecagonal numbers<sup id="cite_ref-560" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-560">[560]</a></sup></dd> <dd><b>1944</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/3-smooth" class="mw-redirect" title="3-smooth">3-smooth</a> number (2<sup>3</sup>×3<sup>5</sup>), <a target="_blank" href="https://en.wikipedia.org/wiki/Achilles_number" title="Achilles number">Achilles number</a><sup id="cite_ref-Achilles_305-1" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Achilles-305">[305]</a></sup></dd> <dd><b>1945</b> = number of partitions of 25 into relatively prime parts such that multiplicities of parts are also relatively prime<sup id="cite_ref-561" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-561">[561]</a></sup></dd> <dd><b>1946</b> = number of surface points on a cube with edge-length 19<sup id="cite_ref-A005897_16-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-A005897-16">[16]</a></sup></dd> <dd><b>1947</b> = k such that 5·2<sup>k</sup> + 1 is a prime factor of a Fermat number 2<sup>2<sup>m</sup></sup> + 1 for some m<sup id="cite_ref-562" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-562">[562]</a></sup></dd> <dd><b>1948</b> = number of strict solid partitions of 20<sup id="cite_ref-563" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-563">[563]</a></sup></dd> <dd><b>1949</b> = smallest prime > 44<sup>2</sup>.<sup id="cite_ref-564" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-564">[564]</a></sup></dd> <dd><b>1950</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1\cdot 2\cdot 3+4\cdot 5\cdot 6+7\cdot 8\cdot 9+10\cdot 11\cdot 12}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>⋅</mo> <mn>2</mn> <mo>⋅</mo> <mn>3</mn> <mo>+</mo> <mn>4</mn> <mo>⋅</mo> <mn>5</mn> <mo>⋅</mo> <mn>6</mn> <mo>+</mo> <mn>7</mn> <mo>⋅</mo> <mn>8</mn> <mo>⋅</mo> <mn>9</mn> <mo>+</mo> <mn>10</mn> <mo>⋅</mo> <mn>11</mn> <mo>⋅</mo> <mn>12</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1\cdot 2\cdot 3+4\cdot 5\cdot 6+7\cdot 8\cdot 9+10\cdot 11\cdot 12}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2bfbbfd62175efeda9715c55cd92aafdd973c3c" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-0.505ex;width:39.391ex;height:2.343ex" alt="{\displaystyle 1\cdot 2\cdot 3+4\cdot 5\cdot 6+7\cdot 8\cdot 9+10\cdot 11\cdot 12}"></span>,<sup id="cite_ref-565" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-565">[565]</a></sup> largest number not the sum of distinct pentadecagonal numbers<sup id="cite_ref-566" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-566">[566]</a></sup></dd> <dd><b>1951</b> = cuban prime<sup id="cite_ref-Cuban_Prime_352-2" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Cuban_Prime-352">[352]</a></sup></dd> <dd><b>1952</b> = number of covers of {1, 2, 3, 4}<sup id="cite_ref-567" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-567">[567]</a></sup></dd> <dd><b>1953</b> = triangular number</dd> <dd><b>1956</b> = number of sum-free subsets of {1, ..., 16}<sup id="cite_ref-568" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-568">[568]</a></sup></dd> <dd><b>1955</b> = number of partitions of 25 with at least one distinct part<sup id="cite_ref-569" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-569">[569]</a></sup></dd> <dd><b>1956</b> = nonagonal number<sup id="cite_ref-Nonagonal_number_151-5" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Nonagonal_number-151">[151]</a></sup></dd> <dd><b>1957</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{k=0}^{6}{\frac {6!}{k!}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mo>!</mo> </mrow> <mrow> <mi>k</mi> <mo>!</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=0}^{6}{\frac {6!}{k!}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c192017b245617f04a7ce5da5801539be31f7fa1" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-3.171ex;width:6.436ex;height:7.509ex" alt="{\displaystyle \sum _{k=0}^{6}{\frac {6!}{k!}}}"></span> = total number of ordered k-tuples (k=0,1,2,3,4,5,6) of distinct elements from an 6-element set<sup id="cite_ref-570" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-570">[570]</a></sup></dd> <dd><b>1958</b> = number of partitions of 25<sup id="cite_ref-571" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-571">[571]</a></sup></dd> <dd><b>1959</b> = Heptanacci-Lucas number<sup id="cite_ref-572" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-572">[572]</a></sup></dd> <dd><b>1960</b> = number of parts in all partitions of 33 into distinct parts<sup id="cite_ref-573" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-573">[573]</a></sup></dd> <dd><b>1961</b> = number of lattice points inside a circle of radius 25<sup id="cite_ref-574" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-574">[574]</a></sup></dd> <dd><b>1962</b> = number of edges in the join of the complete graph K<sub>36</sub> and the cycle graph C<sub>36</sub><sup id="cite_ref-575" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-575">[575]</a></sup></dd> <dd><b>1963</b>! - 1 is prime<sup id="cite_ref-576" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-576">[576]</a></sup></dd> <dd><b>1964</b> = number of linear forests of planted planar trees with 8 nodes<sup id="cite_ref-577" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-577">[577]</a></sup></dd> <dd><b>1965</b> = total number of parts in all partitions of 17<sup id="cite_ref-578" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-578">[578]</a></sup></dd> <dd><b>1966</b> = sum of totient function for first 80 integers</dd> <dd><b>1967</b> = least edge-length of a square dissectable into at least 30 squares in the Mrs. Perkins's quilt problem<sup id="cite_ref-579" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-579">[579]</a></sup></dd> <dd><b>σ(1968)</b> = σ(1967) + σ(1966)<sup id="cite_ref-580" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-580">[580]</a></sup></dd> <dd><b>1969</b> = Only value less than four million for which a "mod-ification" of the standard <a target="_blank" href="https://en.wikipedia.org/wiki/Ackermann_Function" class="mw-redirect" title="Ackermann Function">Ackermann Function</a> does not stabilize<sup id="cite_ref-581" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-581">[581]</a></sup></dd> <dd><b>1970</b> = number of compositions of two types of 9 having no even parts<sup id="cite_ref-582" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-582">[582]</a></sup></dd> <dd><b>1971</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3^{7}-6^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mo>−</mo> <msup> <mn>6</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3^{7}-6^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3d00f2dff691fd38a6d577ec334d6f1bd2f4da7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-0.505ex;width:7.274ex;height:2.843ex" alt="{\displaystyle 3^{7}-6^{3}}"></span><sup id="cite_ref-583" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-583">[583]</a></sup></dd> <dd><b>1972</b> = n such that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {n^{37}-1}{n-1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>37</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {n^{37}-1}{n-1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5ec4d948a8cf06c0fcf46d5be55c8db4b158c1b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-2.005ex;width:8.11ex;height:5.843ex" alt="{\displaystyle {\frac {n^{37}-1}{n-1}}}"></span> is prime<sup id="cite_ref-584" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-584">[584]</a></sup></dd> <dd><span class="anchor" id="1973"></span> <b>1973</b> = Sophie Germain prime, <a target="_blank" href="https://en.wikipedia.org/wiki/Leonardo_prime" class="mw-redirect" title="Leonardo prime">Leonardo prime</a></dd> <dd><b>1974</b> = number of binary vectors of length 17 containing no singletons<sup id="cite_ref-585" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-585">[585]</a></sup></dd> <dd><b>1975</b> = number of partitions of 28 with nonnegative rank<sup id="cite_ref-586" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-586">[586]</a></sup></dd> <dd><b>1976</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Octagonal_number" title="Octagonal number">octagonal number</a><sup id="cite_ref-587" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-587">[587]</a></sup></dd> <dd><b>1977</b> = number of non-isomorphic multiset partitions of weight 9 with no singletons<sup id="cite_ref-588" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-588">[588]</a></sup></dd> <dd><b>1978</b> = n such that n | (3<sup>n</sup> + 5)<sup id="cite_ref-589" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-589">[589]</a></sup></dd> <dd><b>1979</b> = number of squares between 45<sup>2</sup> and 45<sup>4</sup>.<sup id="cite_ref-590" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-590">[590]</a></sup></dd> <dd><b>1980</b> = pronic number<sup id="cite_ref-pronic_number_48-12" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-pronic_number-48">[48]</a></sup></dd> <dd><b>1981</b> = pinwheel number<sup id="cite_ref-Pinwheel_87-8" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Pinwheel-87">[87]</a></sup></dd> <dd><b>1982</b> = maximal number of regions the plane is divided into by drawing 45 circles<sup id="cite_ref-591" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-591">[591]</a></sup></dd> <dd><b>1983</b> = skiponacci number<sup id="cite_ref-592" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-592">[592]</a></sup></dd> <dd><b>1984</b> = 11111000000 in <a target="_blank" href="https://en.wikipedia.org/wiki/Binary_numeral_system" class="mw-redirect" title="Binary numeral system">binary</a>, see also: <a target="_blank" href="https://en.wikipedia.org/wiki/1984_(disambiguation)" class="mw-disambig" title="1984 (disambiguation)">1984 (disambiguation)</a></dd> <dd><b>1985</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Centered_square_number" title="Centered square number">centered square number</a><sup id="cite_ref-Centered_square_numbers_12-9" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-Centered_square_numbers-12">[12]</a></sup></dd> <dd><b>1986</b> = number of ways to write 25 as an orderless product of orderless sums<sup id="cite_ref-593" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-593">[593]</a></sup></dd> <dd><b><a target="_blank" href="https://en.wikipedia.org/wiki/1987_(number)" title="1987 (number)">1987</a></b> = 300th <a target="_blank" href="https://en.wikipedia.org/wiki/Prime_number" title="Prime number">prime number</a></dd> <dd><b>1988</b> = sum of the first 33 primes</dd> <dd><b>1989</b> = number of 9-step mappings with 4 inputs<sup id="cite_ref-594" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-594">[594]</a></sup></dd> <dd><b>1990</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Stella_octangula_number" title="Stella octangula number">Stella octangula number</a></dd> <dd><b>1991</b> = the 46th <a target="_blank" href="https://en.wikipedia.org/wiki/File:1991_A187220_46.png" title="File:1991 A187220 46.png">Gullwing</a> number,<sup id="cite_ref-595" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-595">[595]</a></sup> palindromic composite number with only palindromic prime factors<sup id="cite_ref-596" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-596">[596]</a></sup></dd> <dd><b>1992</b> = number of nonisomorphic sets of nonempty subsets of a 4-set<sup id="cite_ref-597" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-597">[597]</a></sup></dd> <dd><b>1993</b> = a number with the property that 4<sup>1993</sup> - 3<sup>1993</sup> is prime,<sup id="cite_ref-598" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-598">[598]</a></sup> number of partitions of 30 into a prime number of parts<sup id="cite_ref-599" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-599">[599]</a></sup></dd> <dd><b>1994</b> = Glaisher's function W(37)<sup id="cite_ref-600" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-600">[600]</a></sup></dd> <dd><b>1995</b> = number of unlabeled graphs on 9 vertices with independence number 6<sup id="cite_ref-601" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-601">[601]</a></sup></dd> <dd><b>1996</b> = a number with the property that (1996! + 3)/3 is prime<sup id="cite_ref-602" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-602">[602]</a></sup></dd> <dd><b>1997</b> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display:none"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{k=1}^{21}{k\cdot \phi (k)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>21</mn> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>⋅</mo> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{k=1}^{21}{k\cdot \phi (k)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/245df46b6cc36a34a5c4bfd696bd11b3fda642ca" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align:-3.005ex;width:11.038ex;height:7.343ex" alt="{\displaystyle \sum _{k=1}^{21}{k\cdot \phi (k)}}"></span><sup id="cite_ref-603" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-603">[603]</a></sup></dd> <dd><b>1998</b> = triangular matchstick number<sup id="cite_ref-auto5_45-10" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-auto5-45">[45]</a></sup></dd> <dd><b>1999</b> = <a target="_blank" href="https://en.wikipedia.org/wiki/Centered_triangular_number" title="Centered triangular number">centered triangular number</a><sup id="cite_ref-604" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-604">[604]</a></sup> number of <a target="_blank" href="https://en.wikipedia.org/wiki/Regular_polygon" title="Regular polygon">regular</a> forms in a <a target="_blank" href="https://en.wikipedia.org/wiki/Myriagon" title="Myriagon">myriagram</a>.</dd></dl> <h3><span class="mw-headline" id="Prime_numbers">Prime numbers</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a target="_blank" href="https://en.wikipedia.org/w/index.php?title=1000_(number)&action=edit§ion=14" title="Edit section: Prime numbers">edit</a><span class="mw-editsection-bracket">]</span></span></h3> <p>There are 135 <a target="_blank" href="https://en.wikipedia.org/wiki/Prime_number" title="Prime number">prime numbers</a> between 1000 and 2000:<sup id="cite_ref-605" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-605">[605]</a></sup><sup id="cite_ref-606" class="reference"><a target="_blank" href="https://en.wikipedia.org/wiki/1000_(number)#cite_note-606">[606]</a></sup> </p> <dl><dd>1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999</dd></dl> <h2><span class="mw-headline" id="References">References</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a target="_blank" href="https://en.wikipedia.org/w/index.php?title=1000_(number)&action=edit§ion=15" title="Edit section: References">edit</a><span class="mw-editsection-bracket">]</span></span></h2> <link rel="mw-deduplicated-inline-style"><div class="side-box side-box-right plainlinks sistersitebox"> <div class="side-box-flex"> <div class="side-box-image"><img alt="" src="https://upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="noviewer" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376"></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight:bold;font-style:italic"><a target="_blank" href="https://commons.wikimedia.org/wiki/Category:1000_(number)" class="extiw" title="commons:Category:1000 (number)">1000 (number)</a></span>.</div></div> </div> <style data-mw-deduplicate="TemplateStyles:r1093669538">.mw-parser-output .portalbox{padding:0}.mw-parser-output .portalborder{border:solid #aaa 1px}.mw-parser-output .portalbox.tleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalbox.tright{margin:0.5em 0 0.5em 1em}.mw-parser-output .portalbox>ul{display:table;box-sizing:border-box;max-width:175px;font-size:85%;line-height:110%;font-style:italic;font-weight:bold}.mw-parser-output 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Is 1000 a natural number?1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
Is 1000 a whole number?One thousand is shown as 1,000. You would have to count one thousand whole numbers starting from zero and ending with one thousand, just like you would count ten whole numbers to count from zero to ten. A whole number is any number that is not a fraction or decimal.
What is 1000 also called?A thousand is a number equal to 10 times 100. In numerals, it's 1,000 or 1000. The word thousand is almost always preceded by the word a (as in a thousand, which means the same thing as 1,000) or by another number, as in two thousand (2,000), ten thousand (10,000), or nine hundred ninety-nine thousand (999,000).
What are the types of numbers?What does it look like?. |
What type of number is 1000?
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