Natural number
Cardinal one thousand Ordinal 1000th Factorization 23 × 53 Divisors 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 Greek numeral ,Α´ Roman numeral M Roman numeral (unicode ) M, m, ↀ Unicode symbol(s)ↀ Greek prefix chilia Latin prefix milli Binary 11111010002 Ternary 11010013 Senary 43446 Octal 17508 Duodecimal 6B412 Hexadecimal 3E816 Tamil ௲ Chinese 千 Punjabi ੧੦੦੦ Devanagari १००० Armenian Ռ Egyptian hieroglyph 𓆼
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 .
A group of one thousand things is sometimes known, from Ancient Greek , as a chiliad .[1] Latin , as a millennium . The number 1000 is also sometimes described as a short thousand in medieval contexts where it is necessary to distinguish the Germanic concept of 1200 as a long thousand .
Properties
1000 is the 10th icositetragonal number, or 24-gonal number.[2] [3]
1000 is the Wiener index of cycle length 20 , also the sum of labeled boxes arranged as a pyramid with base 1 – 20.[4] [5] [6] [a]
1000 is the element of multiplicity in a
24
×
24
{\displaystyle 24\times 24}
toroidal board in the n -Queens problem[8] indicator of 25 [9] count of 51 .[10] [11]
1000 is the number of strict partitions of 50 containing the sum of no subset of the parts .[12]
The regular polygram {1000/499} of the chiliagon , where its diagonals do not pass through the center , yet are closest to it (indistinguishably, unless one zooms in) A chiliagon polygon ,[13] [14] order 2000 in its regular form .[b]
Totient values
1000 has a reduced totient value
λ
(
n
)
{\displaystyle \lambda (n)}
100 ,[20] Euler totient
φ
(
n
)
{\displaystyle \varphi (n)}
400 .[16]
11 integers have a totient value of 1000 (1111, 1255, ..., 3750).[16]
One thousand is also equal to the sum of Euler's totient summatory function
Φ
(
n
)
{\displaystyle \Phi (n)}
57 integers.[21]
Repdigits
In decimal , multiples of one thousand are totient values of four-digit repdigits :[16]
Notice, that in the list of composite numbers , 7777 is very nearly the composite index of 8888: 8886 is the 7779th composite number.[22] [16]
5000 has a totient value of 2000, as does 5050 = 2025 + 3025 = 45 2 + 55 2 , where3000 , 5000 and 7000 are the three multiples of one thousand, less than 104 , to not be totient values of four-digit repdigits;10000 4 .1600 = 40 2 is the totient value of 4000, as well as 6000, whose collective sum is 10000, where 6000 is the totient of 9999, one less than 104 .[16] [c]
The sum of the first nine prime numbers up to 23 is 100, with
φ
(
p
(
23
)
)
=
1000
{\displaystyle \varphi (p(23))=1000}
p
(
23
)
=
1255
{\displaystyle p(23)=1255}
integer partitions of 23.[28]
Prime values
Using decimal representation as well,
997 is the 168th and largest prime number less than 1000 ,[25] 97 is the 25th and largest prime number less than 100 9 and 7 respectively the (4th) largest composite and prime less than 10 [22] [25] On the other hand, the largest prime number less than 10000 is the 1229th prime number, 9973 .[25] [d]
1000 is also the smallest number in base-ten that generates three primes in the fastest way possible by concatenation with decremented numbers:[37]
1,000,999 1,000,999,998,997 1,000,999,998,997,996,995,994,993 all represent prime numbers.[38] [39]
The one-thousandth prime number is 7919 1 from the order of the smallest sporadic group :
|
M
11
|
=
7920
{\displaystyle |\mathrm {M} _{11}|=7920}
[40] [41]
Numbers in the range 1001–1999
1001 to 1099
1001 sphenic number (7 × 11 × 13), pentagonal number , pentatope number , palindromic number 1002 = sphenic number, Mertens function zero, abundant number , number of partitions of 221003 = the product of some prime p and the p th prime, namely p = 17.1004 = heptanacci number [42] 1005 = Mertens function zero, decagonal pyramidal number[43] 1006 = semiprime , product of two distinct isolated primes (2 and 503); unusual number ; square-free number ; number of compositions (ordered partitions ) of 22 into squares; sum of two distinct pentatope numbers (5 and 1001); number of undirected Hamiltonian paths in 4 by 5 square grid graph ;[44] twin primes ;[45] [46] equidigital number ; when turned around, the number looks like a prime, 9001; its cube can be concatenated from other cubes, 1_0_1_8_1_0_8_216 ("_" indicates concatenation, 0 = 03 , 1 = 13 , 8 = 23 , 216 = 63 )[47] 1007 = number that is the sum of 8 positive 5th powers[48] 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,[49] 1011 = the largest n such that 2n contains 101 and does not 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 [50] 1012 = ternary number, (3210 ) quadruple triangular number (triangular number is 253 ),[51] Egyptian fraction [50] 1013 = Sophie Germain prime ,[52] centered square number ,[53] 1014 = 210 -10,[54] sum of the nontriangular numbers between successive triangular numbers 1015 = square pyramidal number [55] 1016 = member of the Mian–Chowla sequence ,[56] stella octangula number , number of surface points on a cube with edge-length 14[57] 1017 = generalized triacontagonal number[58] 1018 = Mertens function zero, 101816 + 1 is prime[59] 1019 = Sophie Germain prime ,[52] safe prime ,[60] Chen prime 1020 = polydivisible number 1021 = twin prime with 1019 . It is also a Lucky prime .1022 = Friedman number 1023 [61] three-dimensional polycubes with 7 cells;[62] 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 2 = 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 triangle 1026 = 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 .[63] 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 fifth base-10 repunit prime ,[64] Sophie Germain prime ,[52] super-prime , Chen prime 1032 = sum of two distinct powers of 2 (1024 + 8 )1033 = emirp , twin prime with 1031 1034 = sum of 12 positive 9th powers[65] 1035 = triangular number ,[66] hexagonal number [67] 1036 = central polygonal number[68] 1037 = number in E-toothpick sequence[69] 1038 = even integer that is an unordered sum of two primes in exactly n ways[70] 1039 = prime of the form 8n+7,[71] [72] Chen prime 1040 = 45 + 42 : sum of distinct powers of 4.[73] 1041 = sum of 11 positive 5th powers[74] 1042 = sum of 12 positive 5th powers[75] 1043 = number whose sum of even digits and sum of odd digits are even[76] 1044 = sum of distinct powers of 4[73] 1045 = octagonal number [77] 1046 = coefficient of f(q) (3rd order mock theta function)[78] 1047 = number of ways to split a strict composition of n into contiguous subsequences that have the same sum[79] 1048 = number of partitions of n into squarefree parts[80] 1049 = Sophie Germain prime ,[52] highly cototient number ,[81] Chen prime 1050 = 10508 to decimal becomes a pronic number (55210 ),[82] [83] 1051 = centered pentagonal number ,[84] centered decagonal number 1052 = number that is the sum of 9 positive 6th powers[85] 1053 = triangular matchstick number[86] 1054 = centered triangular number [87] 1055 = number that is the sum of 12 positive 6th powers[88] 1056 = pronic number [89] 1057 = central polygonal number[90] 1058 = number that is the sum of 4 positive 5th powers,[91] [92] 1059 = number n such that n4 is written in the form of a sum of four positive 4th powers[93] 1060 = sum of the first 25 primes from 2 through 97 (the number of primes less than 100 ),[94] 23 through 131 .[95] 1061 = emirp , twin prime with 1063 , number of prime numbers having four digits[96] 1062 = number that is not the sum of two palindromes [97] 1063 = super-prime , sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167); near-wall-sun-sun prime[98] 1064 = sum of two positive cubes [99] 1065 = generalized duodecagonal[100] 1066 = number whose sum of their divisors is a square [101] 1067 = number of strict integer partitions of n in which are empty or have smallest part not dividing the other ones[102] 1068 = number that is the sum of 7 positive 5th powers,[46] [103] 1069 = emirp [104] 1070 = number that is the sum of 9 positive 5th powers[105] 1071 = heptagonal number [106] 1072 = centered heptagonal number [107] 1073 = number that is the sum of 12 positive 5th powers[75] 1074 = number that is not the sum of two palindromes [97] 1075 = number non-sum of two palindromes [97] 1076 = number of strict trees weight n [108] 1077 = number where 7 outnumbers every other digit in the number[109] 1078 = Euler transform of negative integers [110] 1079 = every positive integer is the sum of at most 1079 tenth powers.1080 = pentagonal number[111] 1081 = triangular number,[66] Padovan sequence [112] 1082 = central polygonal number[68] 1083 = three-quarter square ,[113] number of partitions of 53 into prime parts 1084 = third spoke of a hexagonal spiral,[114] 108464 + 1 is prime 1085 = number of partitions of n into distinct parts > or = 2 [115] 1086 = Smith number ,[116] 1087 = super-prime, cousin prime , lucky prime [117] 1088 = octo-triangular number , (triangular number result being 136 )[118] 1024 + 64 )[119] primes with the inclusion of multiplicity [120] 1089 2 , nonagonal number , centered octagonal number , first natural number whose digits in its decimal representation get reversed when multiplied by 9.[121] 1090 = sum of 5 positive 5th powers[122] 1091 = cousin prime and twin prime with 1093 1092 = divisible by the number of primes below it1093 Wieferich prime (the only other known Wieferich prime is 3511[123] twin prime with 1091 and star number [124] 1094 = sum of 9 positive 5th powers,[105] 109464 + 1 is prime 1095 = sum of 10 positive 5th powers,[125] palindromes 1096 = hendecagonal number,[126] [127] 1097 = emirp ,[104] Chen prime 1098 = multiple of 9 containing digit 9 in its base-10 representation[128] 1099 = number where 9 outnumbers every other digit[129]
1100 to 1199
1100 = number of partitions of 61 into distinct squarefree parts[130] 1101 = pinwheel number[131] 1102 = sum of totient function for first 60 integers1103 = Sophie Germain prime ,[52] balanced prime [132] 1104 = Keith number [133] 1105 2 + 42 = 322 + 92 = 312 + 122 = 232 + 242 , Carmichael number ,[134] magic constant of n × n normal magic square and n -queens problemn = 13, decagonal number ,[135] [53] Fermat pseudoprime [136] 1106 = number of regions into which the plane is divided when drawing 24 ellipses[137] 1107 = number of non-isomorphic strict T0 multiset partitions of weight 8[138] 1108 = number k such that k64 + 1 is prime 1109 = Friedlander-Iwaniec prime,[139] Chen prime 1110 = k such that 2k + 3 is prime[140] 1111 = 11 × 101, palindrome that is a product of two palindromic primes,[141] repunit [142] 1112 = k such that 9k - 2 is a prime[143] 1113 = number of strict partions of 40[144] 1114 = number of ways to write 22 as an orderless product of orderless sums[145] 1115 = number of partitions of 27 into a prime number of parts[146] 1116 = divisible by the number of primes below it1117 = number of diagonally symmetric polyominoes with 16 cells,[147] Chen prime 1118 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,21}[148] 1119 = number of bipartite graphs with 9 nodes[149] 1120 = number k such that k64 + 1 is prime 1121 = number of squares between 342 and 344 .[150] 1122 = pronic number,[89] 1123 = balanced prime [132] 1124 = Leyland number [151] 10 + 102 , spy number1125 = Achilles number 1126 = number of 2 × 2 non-singular integer matrices with entries from {0, 1, 2, 3, 4, 5}[152] 1127 = maximal number of pieces that can be obtained by cutting an annulus with 46 cuts[153] 1128 = triangular number,[66] [67] 1129 = number of lattice points inside a circle of radius 19[154] 1130 = skiponacci number[155] 1131 = number of edges in the hexagonal triangle T(26)[156] 1132 = number of simple unlabeled graphs with 9 nodes of 2 colors whose components are complete graphs[157] 1133 = number of primitive subsequences of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}[158] 1134 = divisible by the number of primes below it, triangular matchstick number[86] 1135 = centered triangular number [159] 1136 = number of independent vertex sets and vertex covers in the 7-sunlet graph [160] 1137 = sum of values of vertices at level 5 of the hyperbolic Pascal pyramid[161] 1138 = recurring number in the works of George Lucas and his companies, beginning with his first feature film – THX 1138 Star Wars 1139 = wiener index of the windmill graph D(3,17)[162] 1140 = tetrahedral number [163] 1141 = 7-Knödel number[164] 1142 = n such that n32 + 1 is prime,[165] 1143 = number of set partitions of 8 elements with 2 connectors[166] 1144 is not the sum of a pair of twin primes[167] 1145 = 5-Knödel number [168] 1146 is not the sum of a pair of twin primes[167] 1147 = 31 × 37 (a product of 2 successive primes)[169] 1148 is not the sum of a pair of twin primes[167] 1149 = a product of two palindromic primes[170] 1150 = number of 11-iamonds without bilateral symmetry.[171] 1151 = first prime following a prime gap of 22,[172] Chen prime 1152 = highly totient number ,[173] 3-smooth number (27 ×32 ), area of a square with diagonal 48,[92] Achilles number 1153 = super-prime , Proth prime [174] 1154 = 2 × 242 + 2 = number of points on surface of tetrahedron with edgelength 24[175] 1155 = number of edges in the join of two cycle graphs, both of order 33[176] 1156 = 342 , octahedral number ,[177] [84] [178] 1157 = smallest number that can be written as n^2+1 without any prime factors that can be written as a^2+1.[179] 1158 = number of points on surface of octahedron with edgelength 17[180] 1159 = member of the Mian–Chowla sequence,[56] centered octahedral number [181] 1160 = octagonal number [182] 1161 = sum of the first 26 primes1162 = pentagonal number,[111] 1163 = smallest prime > 342 .[183] Legendre's conjecture . Chen prime .1164 = number of chains of multisets that partition a normal multiset of weight 8, where a multiset is normal if it spans an initial interval of positive integers[184] 1165 = 5-Knödel number [168] 1166 = heptagonal pyramidal number[185] 1167 = number of rational numbers which can be constructed from the set of integers between 1 and 43[186] 1168 = antisigma(49)[187] 1169 = highly cototient number[81] 1170 = highest possible score in a National Academic Quiz Tournaments (NAQT) match1171 = super-prime1172 = number of subsets of first 14 integers that have a sum divisible by 14[188] 1173 = number of simple triangulation on a plane with 9 nodes[189] 1174 = number of widely totally strongly normal compositions of 16 1175 = maximal number of pieces that can be obtained by cutting an annulus with 47 cuts[153] 1176 = triangular number[66] 1177 = heptagonal number[106] 1178 = number of surface points on a cube with edge-length 15[57] 1179 = number of different permanents of binary 7*7 matrices[190] 1180 = smallest number of non-integral partitions into non-integral power >1000.[191] 1181 = smallest k over 1000 such that 8*10^k-49 is prime.[192] 1182 = number of necklaces possible with 14 beads of 2 colors (that cannot be turned over)[193] 1183 = pentagonal pyramidal number 1184 = amicable number with 1210[194] 1185 = number of partitions of 45 into pairwise relatively prime parts[195] 1186 = number of diagonally symmetric polyominoes with 15 cells,[147] number of partitions of 54 into prime parts 1187 = safe prime,[60] Stern prime ,[196] [132] Chen prime 1188 = first 4 digit multiple of 18 to contain 18[197] 1189 = number of squares between 352 and 354 .[150] 1190 = pronic number,[89] [198] 1191 = 352 - 35 + 1 = H35 (the 35th Hogben number)[199] 1192 = sum of totient function for first 62 integers1193 = a number such that 41193 - 31193 is prime , Chen prime 1194 =number of permutations that can be reached with 8 moves of 2 bishops and 1 rook on a 3 × 3 chessboard[200] 1195 = smallest four digit number for which a−1 (n) is an integer is a(n) is 2*a(n-1) - (-1)n [201] 1196 =
∑
k
=
1
38
σ
(
k
)
{\displaystyle \sum _{k=1}^{38}\sigma (k)}
[202] 1197 = pinwheel number[131] 1198 = centered heptagonal number[107] 1199 = area of the 20th conjoined trapezoid [203]
1200 to 1299
1200 = the long thousand long hundreds " of 120 each, the traditional reckoning of large numbers in Germanic languages , the number of households the Nielsen ratings sample,[204] number k such that k64 + 1 is prime 1201 = centered square number,[53] super-prime , centered decagonal number 1202 = number of regions the plane is divided into by 25 ellipses[137] 1203 : first 4 digit number in the coordinating sequence for the (2,6,∞) tiling of the hyperbolic plane[205] 1204 : magic constant of a 7 × 7 × 7 magic cube[206] 1205 = number of partitions of 28 such that the number of odd parts is a part[207] 1206 = 29-gonal number [208] 1207 = composite de Polignac number [209] 1208 = number of strict chains of divisors starting with the superprimorial A006939(3)[210] 1209 = The product of all ordered non-empty subsets of {3,1} if {a,b} is a||b: 1209=1*3*13*311210 = amicable number with 1184[211] 1211 = composite de Polignac number [209] 1212 =
∑
k
=
0
17
p
(
k
)
{\displaystyle \sum _{k=0}^{17}p(k)}
p
{\displaystyle p}
k
{\displaystyle k}
[212] 1213 = emirp 1214 = sum of first 39 composite numbers,[213] 1215 = number of edges in the hexagonal triangle T(27)[156] 1216 = nonagonal number[214] 1217 = super-prime , Proth prime[174] 1218 = triangular matchstick number[86] 1219 = Mertens function zero, centered triangular number [159] 1220 = Mertens function zero, number of binary vectors of length 16 containing no singletons[215] 1221 = product of the first two digit, and three digit repdigit1222 = hexagonal pyramidal number 1223 = Sophie Germain prime ,[52] [132] 1224 = number of edges in the join of two cycle graphs, both of order 34[176] 1225 = 352 , square triangular number ,[216] [67] [217] [218] [219] 1226 = number of rooted identity trees with 15 nodes [220] 1227 = smallest number representable as the sum of 3 triangular numbers in 27 ways[221] 1228 = sum of totient function for first 63 integers1229 = Sophie Germain prime ,[52] emirp 1230 = the Mahonian number: T(9, 6)[222] 1231 = smallest mountain emirp, as 121, smallest mountain number is 11 × 111232 = number of labeled ordered set of partitions of a 7-set into odd parts[223] 1233 = 122 + 332 1234 = number of parts in all partitions of 30 into distinct parts,[83] 1235 = excluding duplicates, contains the first four Fibonacci numbers [224] 1236 = 617 + 619: sum of twin prime pair[225] 1237 = prime of the form 2p-11238 = number of partitions of 31 that do not contain 1 as a part[72] 1239 = toothpick number in 3D[226] 1240 = square pyramidal number[55] 1241 = centered cube number ,[227] 1242 = decagonal number[135] 1243 = composite de Polignac number [209] 1244 = number of complete partitions of 25[228] 1245 = Number of labeled spanning intersecting set-systems on 5 vertices.[229] 1246 = number of partitions of 38 such that no part occurs more than once[230] 1247 = pentagonal number[111] 1248 = the first four powers of 2 concatenated together1249 = emirp, trimorphic number [231] 1250 = area of a square with diagonal 50[92] 1251 = 2 × 252 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 25[232] 1252 = 2 × 252 + 2 = number of points on surface of tetrahedron with edgelength 25[175] 1253 = number of partitions of 23 with at least one distinct part[233] 1254 = number of partitions of 23 into relatively prime parts[234] 1255 = Mertens function zero, number of ways to write 23 as an orderless product of orderless sums,[145] [235] 1256 = 1 × 2 × (52 )2 + 6,[236] 1257 = number of lattice points inside a circle of radius 20[154] 1258 = 1 × 2 × (52 )2 + 8,[236] 1259 = highly cototient number [81] 1260 = highly composite number ,[237] [89] vampire number ,[238] [144] Book of Revelation 1261 = star number,[124] 1262 = maximal number of regions the plane is divided into by drawing 36 circles[239] 1263 = rounded total surface area of a regular tetrahedron with edge length 27[240] 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[241] 1266 = centered pentagonal number,[84] 1267 = 7-Knödel number[164] 1268 = number of partitions of 37 into prime power parts[242] 1269 = least number of triangles of the Spiral of Theodorus to complete 11 revolutions[243] 1270 = 25 + 24×26 + 23×27,[244] 1271 = sum of first 40 composite numbers[213] 1272 = sum of first 41 nonprimes[245] 1273 = 19 × 67 = 19 × prime(19)[246] 1274 = sum of the nontriangular numbers between successive triangular numbers 1275 = triangular number,[66] 1276 = number of irredundant sets in the 25-cocktail party graph[247] 1277 = the start of a prime constellation of length 9 (a "prime nonuple")1278 = number of Narayana's cows and calves after 20 years[248] 1279 = Mertens function zero, Mersenne prime exponent1280 = Mertens function zero, number of parts in all compositions of 9[249] 1281 = octagonal number [182] 1282 = Mertens function zero, number of partitions of 46 into pairwise relatively prime parts[195] 1283 = safe prime[60] 1284 = 641 + 643: sum of twin prime pair[225] 1285 = Mertens function zero, number of free nonominoes , number of parallelogram polyominoes with 10 cells.[250] 1286 = number of inequivalent connected planar figures that can be formed from five 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree[251] 1287 =
(
13
5
)
{\displaystyle {13 \choose 5))
[252] 1288 = heptagonal number[106] 1289 [52] 1290 =
1289
+
1291
2
{\displaystyle {\frac {1289+1291}{2))}
[253] 1291 = largest prime < 64 ,[254] 1292 = number such that phi(1292) = phi(sigma(1292)),[255] 1293 =
∑
j
=
1
n
j
×
p
r
i
m
e
(
j
)
{\displaystyle \sum _{j=1}^{n}j\times prime(j)}
[256] 1294 = rounded volume of a regular octahedron with edge length 14[257] 1295 = number of edges in the join of two cycle graphs, both of order 35[176] 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 InDesign, number of combinations of 2 characters(00-ZZ)1297 = super-prime , Mertens function zero, pinwheel number[131] 1298 = number of partitions of 55 into prime parts 1299 = Mertens function zero, number of partitions of 52 such that the smallest part is greater than or equal to number of parts[258]
1300 to 1399
1300 = Sum of the first 4 fifth powers, mertens function zero, largest possible win margin in an NAQT match; smallest even odd-factor hyperperfect number1301 = centered square number,[53] [259] [260] 1302 = Mertens function zero, number of edges in the hexagonal triangle T(28)[156] 1303 = prime of form 21n+1 and 31n+1[261] [262] 1304 = sum of 13046 and 1304 9 which is 328+9761305 = triangular matchstick number[86] 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 .[159] 1307 = safe prime[60] 1308 = sum of totient function for first 65 integers1309 = the first sphenic number followed by two consecutive such number1310 = smallest number in the middle of a set of three sphenic numbers1311 = number of integer partitions of 32 with no part dividing all the others[263] 1312 = member of the Mian-Chowla sequence;[56] 1313 = sum of all parts of all partitions of 14 [264] 1314 = number of integer partitions of 41 whose distinct parts are connected[265] 1315 = 10^(2n+1)-7*10^n-1 is prime.[266] 1316 = Euler transformation of sigma(11)[267] 1317 = 1317 Only odd four digit number to divide the concatenation of all number up to itself in base 25[268] 1318 512 + 1 is prime,[269] 1319 = safe prime[60] 1320 = 659 + 661: sum of twin prime pair[225] 1321 = Friedlander-Iwaniec prime[139] 1322 = area of the 21st conjoined trapezoid [203] 1323 = Achilles number 1324 = if D(n) is the nth representation of 1, 2 arranged lexicographically. 1324 is the first non-1 number which is D(D(x))[270] 1325 = Markov number ,[271] [272] 1326 = triangular number,[66] [67] 1327 = 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[213] 1330 = tetrahedral number,[151] Ruth–Aaron pair with 1331 under second definition1331 = 113 , centered heptagonal number,[107] x 2 + x − 1, for x = 36.1332 = pronic number[89] 1333 = 372 - 37 + 1 = H37 (the 37th Hogben number)[199] 1334 = maximal number of regions the plane is divided into by drawing 37 circles[239] 1335 = pentagonal number,[111] 1336 = sum of gcd(x, y) for 1 <= x, y <= 24,[273] 1337 = Used in the novel form of spelling called leet . Approximate melting point of gold in kelvins .1338 = atomic number of the noble element of period 18,[274] 1339 = First 4 digit number to appear twice in the sequence of sum of cubes of primes dividing n[275] 1340 = k such that 5 × 2k - 1 is prime[276] 1341 = First mountain number with 2 jumps of more than one.1342 =
∑
k
=
1
40
σ
(
k
)
{\displaystyle \sum _{k=1}^{40}\sigma (k)}
[202] 1343 = cropped hexagone [277] 1344 = 372 - 52 , the only way to express 1344 as a difference of prime squares[278] 1345 = k such that k, k+1 and k+2 are products of two primes[279] 1346 = number of locally disjointed rooted trees with 10 nodes[280] 1347 = concatenation of first 4 Lucas numbers [281] 1348 = number of ways to stack 22 pennies such that every penny is in a stack of one or two[282] 1349 = Stern-Jacobsthal number[283] 1350 = nonagonal number[214] 1351 = number of partitions of 28 into a prime number of parts[146] 1352 = number of surface points on a cube with edge-length 16,[57] Achilles number 1353 = 2 × 262 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 26[232] 1354 = 2 × 262 + 2 = number of points on surface of tetrahedron with edgelength 26[175] 1355 appears for the first time in the Recamán's sequence at n = 325,374,625,245.[284] [285] [286] 1356 is not the sum of a pair of twin primes[167] 1357 = number of nonnegative solutions to x2 + y2 ≤ 412 [287] 1358 = rounded total surface area of a regular tetrahedron with edge length 28[240] 1359 is the 42d term of Flavius Josephus's sieve[288] 1360 = 372 - 32 , the only way to express 1360 as a difference of prime squares[278] 1361 = first prime following a prime gap of 34,[172] centered decagonal number , 3rd Mills' prime , Honaker prime[259] 1362 = number of achiral integer partitions of 48[289] 1363 = the number of ways to modify a circular arrangement of 14 objects by swapping one or more adjacent pairs[290] 1364 = Lucas number[291] 1365 = pentatope number[292] 1366 = Arima number, after Yoriyuki Arima who in 1769 constructed this sequence as the number of moves of the outer ring in the optimal solution for the Chinese Rings puzzle[293] 1367 = safe prime,[60] [132] 1368 = number of edges in the join of two cycle graphs, both of order 36[176] 1369 = 372 , centered octagonal number[217] 1370 = σ2 (37): sum of squares of divisors of 37[294] 1371 = sum of the first 28 primes1372 = Achilles number 1373 = number of lattice points inside a circle of radius 21[154] 1374 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,23}[148] 1375 = decagonal pyramidal number[295] 1376 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers )[296] 1377 = maximal number of pieces that can be obtained by cutting an annulus with 51 cuts[153] 1378 = triangular number[66] 1379 = magic constant of n × n normal magic square and n -queens problemn = 14.1380 = number of 8-step mappings with 4 inputs[297] 1381 = centered pentagonal number[84] 1382 = first 4 digit tetrachi number [298] 1383 = 3 × 461. 101383 + 7 is prime[299] 1384 =
∑
k
=
1
41
σ
(
k
)
{\displaystyle \sum _{k=1}^{41}\sigma (k)}
[202] 1385 = up/down number[300] 1386 = octagonal pyramidal number[301] 1387 = 5th Fermat pseudoprime of base 2,[302] centered hexagonal number and the 19th decagonal number ,[135] Super-Poulet number .[303] 1388 = 4 × 192 - 3 × 19 + 1 and is therefore on the x-axis of Ulams spiral [304] 1389 = sum of first 42 composite numbers[213] 1390 = sum of first 43 nonprimes[245] 1391 = number of rational numbers which can be constructed from the set of integers between 1 and 47[186] 1392 = number of edges in the hexagonal triangle T(29)[156] 1393 = 7-Knödel number[164] 1394 = sum of totient function for first 67 integers1395 = vampire number ,[238] [56] [86] 1396 = centered triangular number [159] 1397 =
⌊
5
9
2
⌋
{\displaystyle \left\lfloor 5^{\frac {9}{2))\right\rfloor }
[305] 1398 = number of integer partitions of 40 whose distinct parts are connected[265] 1399 = emirp[306]
1400 to 1499
1400 = number of sum-free subsets of {1, ..., 15}[307] 1401 = pinwheel number[131] 1402 = number of integer partitions of 48 whose augmented differences are distinct,[308] [309] 1403 = smallest x such that M(x) = 11, where M() is Mertens function [310] 1404 = heptagonal number[106] 1405 = 262 + 272 , 72 + 82 + ... + 162 , centered square number[53] 1406 = pronic number,[89] semi-meandric number [311] 1407 = 382 - 38 + 1 = H38 (the 38th Hogben number)[199] 1408 = maximal number of regions the plane is divided into by drawing 38 circles[239] 1409 = super-prime , Sophie Germain prime,[52] [174] 1410 = denominator of the 46th Bernoulli number [312] 1411 = LS(41)[313] 1412 = LS(42),[313] 1413 = LS(43)[313] 1414 = smallest composite that when added to sum of prime factors reaches a prime after 27 iterations[314] 1415 = the Mahonian number: T(8, 8)[222] 1416 = LS(46)[313] 1417 = number of partitions of 32 in which the number of parts divides 32[315] 1418 = smallest x such that M(x) = 13, where M() is Mertens function [310] 1419 = Zeisel number [316] 1420 = Number of partitions of 56 into prime parts 1421 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 29-manifold to be realizable as a sub-manifold,[317] 1422 = number of partitions of 15 with two parts marked[318] 1423 = 200 + 1223 and the 200th prime is 1223[319] 1424 = number of nonnegative solutions to x2 + y2 ≤ 422 [287] 1425 = self-descriptive number in base 51426 = sum of totient function for first 68 integers, pentagonal number,[111] [144] 1427 = twin prime together with 1429[320] 1428 = number of complete ternary trees with 6 internal nodes, or 18 edges[321] 1429 = number of partitions of 53 such that the smallest part is greater than or equal to number of parts[258] 1430 = Catalan number [322] 1431 = triangular number,[66] [67] 1432 = member of Padovan sequence[112] 1433 = super-prime , Honaker prime,[259] Microsoft SQL Server databases 1434 = rounded volume of a regular tetrahedron with edge length 23[323] 1435 = vampire number ;[238] 8+ 1 ⁄2 inches (1.435 m)1436 = discriminant of a totally real cubic field[324] 1437 = smallest number of complexity 20: smallest number requiring 20 1's to build using +, * and ^[325] 1438 = k such that 5 × 2k - 1 is prime[276] 1439 = Sophie Germain prime,[52] [60] 1440 = a highly totient number [173] gonal number . Also, the number of minutes in one day, the blocksize of a standard 3+ 1 / 2 floppy disk , and the horizontal resolution of WXGA(II) computer displays1441 = star number[124] 1442 = number of parts in all partitions of 31 into distinct parts[83] 1443 = the sum of the second trio of three-digit permutable primes in decimal : 337 , 373 , and 733 . Also the number of edges in the join of two cycle graphs, both of order 37 [176] 1444 = 382 , smallest pandigital number in Roman numerals 1445 =
∑
k
=
0
3
(
(
3
k
)
×
(
3
+
k
k
)
)
2
{\displaystyle \sum _{k=0}^{3}\left({\binom {3}{k))\times {\binom {3+k}{k))\right)^{2))
[326] 1446 = number of points on surface of octahedron with edgelength 19[180] 1447 = super-prime , happy number 1448 = number k such that phi(prime(k)) is a square[327] 1449 = Stella octangula number 1450 = σ2 (34): sum of squares of divisors of 34[294] 1451 = Sophie Germain prime[52] 1452 = first Zagreb index of the complete graph K12 [328] 1453 = Sexy prime with 14591454 = 3 × 222 + 2 = number of points on surface of square pyramid of side-length 22[329] 1455 = k such that geometric mean of phi(k) and sigma(k) is an integer[330] 1456 = number of regions in regular 15-gon with all diagonals drawn[331] 1457 = 2 × 272 − 1 = a twin square [332] 1458 maximum determinant of an 11 by 11 matrix of zeroes and ones, 3-smooth number (2×36 )1459 = Sexy prime with 1453, sum of nine consecutive primes (139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181), pierpont prime 1460 = The number of years that would have to pass in the Julian calendar in order to accrue a full year's worth of leap days.1461 = number of partitions of 38 into prime power parts[242] 1462 = (35 - 1) × (35 + 8) = the first Zagreb index of the wheel graph with 35 vertices[333] 1463 = total number of parts in all partitions of 16[103] 1464 = rounded total surface area of a regular icosahedron with edge length 13[334] 1465 = 5-Knödel number [168] 1466 =
∑
k
=
1
256
d
(
k
)
{\displaystyle \sum _{k=1}^{256}d(k)}
d
(
k
)
{\displaystyle d(k)}
k
{\displaystyle k}
[335] 1467 = number of partitions of 39 with zero crank[336] 1468 = number of polyhexes with 11 cells that tile the plane by translation[337] 1469 = octahedral number,[177] [81] 1470 = pentagonal pyramidal number ,[338] 1471 = super-prime , centered heptagonal number[107] 1472 = number of overpartitions of 15[339] 1473 = cropped hexagone [277] 1474 =
44
(
44
+
1
)
2
+
44
2
4
{\displaystyle {\frac {44(44+1)}{2))+{\frac {44^{2)){4))}
[340] 1475 = number of partitions of 33 into parts each of which is used a different number of times[341] 1476 = coreful perfect number[342] 1477 = 7-Knödel number[164] 1478 = total number of largest parts in all compositions of 11[343] 1479 = number of planar partitions of 12[344] 1480 = sum of the first 29 primes1481 = Sophie Germain prime[52] 1482 = pronic number,[89] [345] 1483 = 392 - 39 + 1 = H39 (the 39th Hogben number)[199] 1484 = maximal number of regions the plane is divided into by drawing 39 circles[239] 1485 = triangular number1486 = number of strict solid partitions of 19[127] 1487 = safe prime[60] 1488 = triangular matchstick number[86] 1489 = centered triangular number [159] 1490 = tetranacci number [346] 1491 = nonagonal number,[214] 1492 = discriminant of a totally real cubic field,[324] 1493 = Stern prime[196] 1494 = sum of totient function for first 70 integers1495 = 9###[347] 1496 = square pyramidal number[55] 1497 = skiponacci number[155] 1498 = number of flat partitions of 41[348] 1499 = Sophie Germain prime,[52] super-prime
1500 to 1599
1500 = hypotenuse in three different Pythagorean triangles[349] 1501 = centered pentagonal number[84] 1502 = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 47[350] 1503 = least number of triangles of the Spiral of Theodorus to complete 12 revolutions[243] 1504 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers )[296] 1505 = number of integer partitions of 41 with distinct differences between successive parts[351] 1506 = number of Golomb partitions of 28[352] 1507 = number of partitions of 32 that do not contain 1 as a part[72] 1508 = heptagonal pyramidal number[185] 1509 = pinwheel number[131] 1510 deficient number , odious number 1511 = Sophie Germain prime,[52] [132] 1512 = k such that geometric mean of phi(k) and sigma(k) is an integer[330] 1513 = centered square number[53] 1514 = sum of first 44 composite numbers[213] 1515 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 30-manifold to be realizable as a sub-manifold[317] 1516 =
⌊
9
10
3
⌋
{\displaystyle \left\lfloor 9^{\frac {10}{3))\right\rfloor }
[353] 1517 = number of lattice points inside a circle of radius 22[154] 1518 = sum of first 32 semiprimes,[354] 1519 = number of polyhexes with 8 cells,[355] 1520 = pentagonal number,[111] 1521 = 392 , Mertens function zero, centered octagonal number,[217] 1522 = k such that 5 × 2k - 1 is prime[276] 1523 = super-prime , Mertens function zero, safe prime,[60] [56] 1524 = Mertens function zero, k such that geometric mean of phi(k) and sigma(k) is an integer[330] 1525 = heptagonal number,[106] 1526 = number of conjugacy classes in the alternating group A27 [356] 1527 = number of 2-dimensional partitions of 11,[357] 1528 = Mertens function zero, rounded total surface area of a regular octahedron with edge length 21[358] 1529 = composite de Polignac number [209] 1530 = vampire number [238] 1531 = prime number, centered decagonal number , Mertens function zero1532 = number of series-parallel networks with 9 unlabeled edges,[359] 1533 = 21 × 73 = 21 × 21st prime[246] 1534 = number of achiral integer partitions of 50[289] 1535 = Thabit number 1536 = a common size of microplate , 3-smooth number (29 ×3), number of threshold functions of exactly 4 variables[360] 1537 = Keith number,[133] 1538 = number of surface points on a cube with edge-length 17[57] 1539 = maximal number of pieces that can be obtained by cutting an annulus with 54 cuts[153] 1540 = triangular number, hexagonal number,[67] [135] [151] 1541 = octagonal number [182] 1542 = k such that 2^k starts with k[361] 1543 = prime dividing all Fibonacci sequences,[362] 1544 = Mertens function zero, number of partitions of integer partitions of 17 where all parts have the same length[363] 1545 = number of reversible string structures with 9 beads using exactly three different colors[364] 1546 = number of 5 X 5 binary matrices with at most one 1 in each row and column,[365] 1547 = hexagonal pyramidal number 1548 = coreful perfect number[342] 1549 = de Polignac prime[366] 1550 =
31
×
(
3
×
31
+
7
)
2
{\displaystyle {\frac {31\times (3\times 31+7)}{2))}
[367] 1551 = 6920 - 5369 = A169952(24) - A169952(23) = A169942(24) = number of Golomb rulers of length 24[368] [369] 1552 = Number of partitions of 57 into prime parts 1553 = 509 + 521 + 523 = a prime that is the sum of three consecutive primes[370] 1554 = 2 × 3 × 7 × 37 = product of four distinct primes[371] 1555 2 divides 61554 [372] 1556 = sum of the squares of the first nine primes1557 = number of graphs with 8 nodes and 13 edges[373] 1558 = number k such that k64 + 1 is prime1559 = Sophie Germain prime[52] 1560 = pronic number[89] 1561 = a centered octahedral number ,[181] [374] 1562 = maximal number of regions the plane is divided into by drawing 40 circles[239] 1563 =
∑
k
=
1
50
50
gcd
(
50
,
k
)
{\displaystyle \sum _{k=1}^{50}{\frac {50}{\gcd(50,k)))}
[375] 1564 = sum of totient function for first 71 integers1565 =
1036
2
+
1173
2
{\displaystyle {\sqrt {1036^{2}+1173^{2))))
1036
+
1173
=
47
2
{\displaystyle 1036+1173=47^{2))
[376] 1566 = number k such that k64 + 1 is prime1567 = number of partitions of 24 with at least one distinct part[233] 1568 = Achilles number [377] 1569 = 2 × 282 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 28[232] 1570 = 2 × 282 + 2 = number of points on surface of tetrahedron with edgelength 28[175] 1571 = Honaker prime[259] 1572 = member of the Mian–Chowla sequence[56] 1573 = discriminant of a totally real cubic field[324] 1574 256 + 1 is prime[378] 1575 = odd abundant number ,[379] sum of the nontriangular numbers between successive triangular numbers , number of partitions of 24[235] 1576 14 == 1 (mod 15^2)[380] 1577 = sum of the quadratic residues of 83[381] 1578 = sum of first 45 composite numbers[213] 1579 = number of partitions of 54 such that the smallest part is greater than or equal to number of parts[258] 1580 = number of achiral integer partitions of 51[289] 1581 = number of edges in the hexagonal triangle T(31)[156] 1582 = a number such that the integer triangle [A070080(1582), A070081(1582), A070082(1582)] has an integer area[382] 1583 = Sophie Germain prime1584 = triangular matchstick number[86] 1585 = Riordan number , centered triangular number [159] 1586 = area of the 23rd conjoined trapezoid [203] 1587 = 3 × 232 = number of edges of a complete tripartite graph of order 69, K23,23,23 [383] 1588 = sum of totient function for first 72 integers1589 = composite de Polignac number [209] 1590 = rounded volume of a regular icosahedron with edge length 9[384] 1591 = rounded volume of a regular octahedron with edge length 15[257] 1592 = sum of all divisors of the first 36 odd numbers[385] 1593 = sum of the first 30 primes1594 = minimal cost of maximum height Huffman tree of size 17[386] 1595 = number of non-isomorphic set-systems of weight 10 1596 = triangular number1597 = Fibonacci prime ,[387] Markov prime ,[271] super-prime , emirp 1598 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,25}[148] 1599 = number of edges in the join of two cycle graphs, both of order 39[176]
1600 to 1699
1600 = 402 , structured great rhombicosidodecahedral number,[388] 7 ), street number on Pennsylvania Avenue of the White House , length in meters of a common High School Track Event, perfect score on SAT (except from 2005 to 2015)1601 = Sophie Germain prime, Proth prime,[174] 1601 (Mark Twain) 1602 = number of points on surface of octahedron with edgelength 20[180] 1603 = number of partitions of 27 with nonnegative rank[389] 1604 = number of compositions of 22 into prime parts[390] 1605 = number of polyominoes consisting of 7 regular octagons[391] 1606 = enneagonal pyramidal number[392] 1607 = member of prime triple with 1609 and 1613[393] 1608 =
∑
k
=
1
44
σ
(
k
)
{\displaystyle \sum _{k=1}^{44}\sigma (k)}
[202] 1609 = cropped hexagonal number [277] 1610 = number of strict partions of 43[144] 1611 = number of rational numbers which can be constructed from the set of integers between 1 and 51[186] 1612 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 31-manifold to be realizable as a sub-manifold[317] 1613 , 1607 and 1619 are all primes[394] 1614 = number of ways of refining the partition 8^1 to get 1^8[395] 1615 = composite number such that the square mean of its prime factors is a nonprime integer[396] 1616 =
16
(
16
2
+
3
×
16
−
1
)
3
{\displaystyle {\frac {16(16^{2}+3\times 16-1)}{3))}
3 [397] 1617 = pentagonal number[111] 1618 = centered heptagonal number[107] 1619 = palindromic prime in binary , safe prime[60] 1620 = 809 + 811: sum of twin prime pair[225] 1621 = super-prime , pinwheel number[131] 1622 = semiprime of the form prime + 1[398] 1623 is not the sum of two triangular numbers and a fourth power[399] 1624 = number of squares in the Aztec diamond of order 28[400] 1625 = centered square number[53] 1626 = centered pentagonal number[84] 1627 = prime and 2 × 1627 - 1 = 3253 is also prime[401] 1628 = centered pentagonal number[84] 1629 = rounded volume of a regular tetrahedron with edge length 24[323] 1630 = number k such that k^64 + 1 is prime 1631 =
∑
k
=
0
5
(
k
+
1
)
!
(
5
k
)
{\displaystyle \sum _{k=0}^{5}(k+1)!{\binom {5}{k))}
[402] 1632 = number of acute triangles made from the vertices of a regular 18-polygon[403] 1633 = star number[124] 1634 = Narcissistic number in base 101635 = number of partitions of 56 whose reciprocal sum is an integer[404] 1636 = number of nonnegative solutions to x2 + y2 ≤ 452 [287] 1637 = prime island: least prime whose adjacent primes are exactly 30 apart[405] 1638 = harmonic divisor number ,[406] 1638 - 1 is prime[276] 1639 = nonagonal number[214] 1640 = pronic number[89] 1641 = 412 - 41 + 1 = H41 (the 41st Hogben number)[199] 1642 = maximal number of regions the plane is divided into by drawing 41 circles[239] 1643 = sum of first 46 composite numbers[213] 1644 = 821 + 823: sum of twin prime pair[225] 1645 = number of 16-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection[407] 1646 = number of graphs with 8 nodes and 14 edges[373] 1647 and 1648 are both divisible by cubes[408] 1648 = number of partitions of 343 into distinct cubes[409] 1649 = highly cototient number,[81] [151] 1650 = number of cards to build an 33-tier house of cards[198] 1651 = heptagonal number[106] 1652 = number of partitions of 29 into a prime number of parts[146] 1653 = triangular number, hexagonal number,[67] [154] 1654 = number of partitions of 42 into divisors of 42[410] 1655 = rounded volume of a regular dodecahedron with edge length 6[411] 1656 = 827 + 829: sum of twin prime pair[225] 1657 = cuban prime ,[412] 1658 = smallest composite that when added to sum of prime factors reaches a prime after 25 iterations[314] 1659 = number of rational numbers which can be constructed from the set of integers between 1 and 52[186] 1660 = sum of totient function for first 73 integers1661 = 11 × 151, palindrome that is a product of two palindromic primes[141] 1662 = number of partitions of 49 into pairwise relatively prime parts[195] 1663 = a prime number and 51663 - 41663 is a 1163-digit prime number[413] 1664 = k such that k, k+1 and k+2 are sums of 2 squares[414] 1665 = centered tetrahedral number[272] 1666 = largest efficient pandigital number in Roman numerals (each symbol occurs exactly once)1667 = 228 + 1439 and the 228th prime is 1439[319] 1668 = number of partitions of 33 into parts all relatively prime to 33[415] 1669 = super-prime , smallest prime with a gap of exactly 24 to the next prime[416] 1670 = number of compositions of 12 such that at least two adjacent parts are equal[417] 1671 divides the sum of the first 1671 composite numbers[418] 1672 = 412 - 32 , the only way to express 1672 as a difference of prime squares[278] 1673 = RMS number[419] 1674 = k such that geometric mean of phi(k) and sigma(k) is an integer[330] 1675 = Kin number[420] 1676 = number of partitions of 34 into parts each of which is used a different number of times[341] 1677 = 412 - 22 , the only way to express 1677 as a difference of prime squares[278] 1678 = n such that n32 + 1 is prime[165] 1679 = highly cototient number,[81] Arecibo message ), number of parts in all partitions of 32 into distinct parts[83] 1680 = highly composite number,[237] [176] 1681 = 412 , smallest number yielded by the formula n 2 + n + 41 that is not a prime; centered octagonal number[217] 1682 = and 1683 is a member of a Ruth–Aaron pair (first definition)1683 = triangular matchstick number[86] 1684 = centered triangular number [159] 1685 = 5-Knödel number [168] 1686 =
∑
k
=
1
45
σ
(
k
)
{\displaystyle \sum _{k=1}^{45}\sigma (k)}
[202] 1687 = 7-Knödel number[164] 1688 = number of finite connected sets of positive integers greater than one with least common multiple 72[421] 1689 =
9
!
!
∑
k
=
0
4
1
2
k
+
1
{\displaystyle 9!!\sum _{k=0}^{4}{\frac {1}{2k+1))}
[422] 1690 = number of compositions of 14 into powers of 2[423] 1691 = the same upside down, which makes it a strobogrammatic number[424] 1692 = coreful perfect number[342] 1693 = smallest prime > 412 .[183] 1694 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,26}[148] 1695 = magic constant of n × n normal magic square and n -queens problemn = 15. Number of partitions of 58 into prime parts 1696 = sum of totient function for first 74 integers1697 = Friedlander-Iwaniec prime[139] 1698 = number of rooted trees with 47 vertices in which vertices at the same level have the same degree[241] 1699 = number of rooted trees with 48 vertices in which vertices at the same level have the same degree[241]
1700 to 1799
1700 = σ2 (39): sum of squares of divisors of 39[294] 1701
{
8
4
}
{\displaystyle \left\((8 \atop 4}\right\))
Star Trek 1702 = palindromic in 3 consecutive bases: 89814 , 78715 , 6A616 1703 = 1703131131 / 1000077 and the divisors of 1703 are 1703, 131, 13 and 1[425] 1704 = sum of the squares of the parts in the partitions of 18 into two distinct parts[426] 1705 = tribonacci number [427] 1706 = 1 + 4 + 16 + 64 + 256 + 1024 + 256 + 64 + 16 + 4 + 1 sum of fifth row of triangle of powers of 4[428] 1707 = number of partitions of 30 in which the number of parts divides 30[315] 1708 = 22 × 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[429] 1709 = first of a sequence of eight primes formed by adding 57 in the middle. 1709, 175709, 17575709, 1757575709, 175757575709, 17575757575709, 1757575757575709 and 175757575757575709 are all prime, but 17575757575757575709 = 232433 × 756164467857731710 = maximal number of pieces that can be obtained by cutting an annulus with 57 cuts[153] 1711 = triangular number, centered decagonal number 1712 = number of irredundant sets in the 29-cocktail party graph[247] 1713 = number of aperiodic rooted trees with 12 nodes[430] 1714 = number of regions formed by drawing the line segments connecting any two of the 18 perimeter points of an 3 × 6 grid of squares [431] 1715 = k such that geometric mean of phi(k) and sigma(k) is an integer[330] 1716 = 857 + 859: sum of twin prime pair[225] 1717 = pentagonal number[111] 1718 =
∑
d
|
12
(
12
d
)
{\displaystyle \sum _{d|12}{\binom {12}{d))}
[432] 1719 = composite de Polignac number [209] 1720 = sum of the first 31 primes1721 = twin prime; number of squares between 422 and 424 .[150] 1722 = Giuga number ,[433] [89] 1723 = super-prime 1724 = maximal number of regions the plane is divided into by drawing 42 circles[239] 1725 = 472 - 222 = (prime(15))2 - (nonprime(15))2 [434] 1726 = number of partitions of 44 into distinct and relatively prime parts[435] 1727 = area of the 24th conjoined trapezoid [203] 1728 duodecimal , that is, the cube of twelve (called a great gross ), and so, the number of cubic inches in a cubic foot , palindromic in base 11 (133111 ) and 23 (36323 )1729 taxicab number , Carmichael number, Zeisel number, centered cube number, Hardy–Ramanujan number . In the decimal expansion of e the first time all 10 digits appear in sequence starts at the 1729th digit (or 1728th decimal place). In 1979 the rock musical Hair 1730 = 3 × 242 + 2 = number of points on surface of square pyramid of side-length 24[329] 1731 = k such that geometric mean of phi(k) and sigma(k) is an integer[330] 1732 =
∑
k
=
0
5
(
5
k
)
k
{\displaystyle \sum _{k=0}^{5}{\binom {5}{k))^{k))
[436] 1733 = Sophie Germain prime , palindromic in bases 3, 18, 19.1734 = surface area of a cube of edge length 17[437] 1735 = number of partitions of 55 such that the smallest part is greater than or equal to number of parts[258] 1736 = sum of totient function for first 75 integers, number of surface points on a cube with edge-length 18[57] 1737 = pinwheel number[131] 1738 = number of achiral integer partitions of 52[289] 1739 = number of 1s in all partitions of 30 into odd parts[438] 1740 = number of squares in the Aztec diamond of order 29[400] 1741 = super-prime , centered square number[53] 1742 = number of regions the plane is divided into by 30 ellipses[137] 1743 = wiener index of the windmill graph D(3,21)[162] 1744 = k such that k, k+1 and k+2 are sums of 2 squares[414] 1745 = 5-Knödel number [168] 1746 = number of unit-distance graphs on 8 nodes[439] 1747 = balanced prime[132] 1748 = number of partitions of 55 into distinct parts in which the number of parts divides 55[440] 1749 = number of integer partitions of 33 with no part dividing all the others[263] 1750 = hypotenuse in three different Pythagorean triangles[349] 1751 = cropped hexagone [277] 1752 = 792 - 672 , the only way to express 1752 as a difference of prime squares[278] 1753 = balanced prime [132] 1754 = k such that 5*2k - 1 is prime[276] 1755 = number of integer partitions of 50 whose augmented differences are distinct[308] 1756 = centered pentagonal number[84] 1757 = least number of triangles of the Spiral of Theodorus to complete 13 revolutions[243] 1758 =
∑
k
=
1
46
σ
(
k
)
{\displaystyle \sum _{k=1}^{46}\sigma (k)}
[202] 1759 = de Polignac prime[366] 1760 = the number of yards in a mile1761 = k such that k, k+1 and k+2 are products of two primes[279] 1762 = number of binary sequences of length 12 and curling number 2 [441] 1763 = number of edges in the join of two cycle graphs, both of order 41[176] 1764 = 422 1765 = number of stacks, or planar partitions of 15[442] 1766 = number of points on surface of octahedron with edgelength 21[180] 1767 = σ(282 ) = σ(352 )[443] 1768 = number of nonequivalent dissections of an hendecagon into 8 polygons by nonintersecting diagonals up to rotation[444] 1769 = maximal number of pieces that can be obtained by cutting an annulus with 58 cuts[153] 1770 = triangular number, hexagonal number,[67] Seventeen Seventy , town in Australia1771 = tetrahedral number[151] 1772 = centered heptagonal number,[107] 1773 = number of words of length 5 over the alphabet {1,2,3,4,5} such that no two even numbers appear consecutively[445] 1774 = number of rooted identity trees with 15 nodes and 5 leaves[446] 1775 =
∑
1
≤
i
≤
10
p
r
i
m
e
(
i
)
⋅
(
2
⋅
i
−
1
)
{\displaystyle \sum _{1\leq i\leq 10}prime(i)\cdot (2\cdot i-1)}
[447] 1776 = square star number .[448] 1777 = smallest prime > 422 .[183] 1778 = least k >= 1 such that the remainder when 6k is divided by k is 22[449] 1779 = number of achiral integer partitions of 53[289] 1780 = 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[450] 1781 = the first 1781 digits of e form a prime[451] 1782 = heptagonal number[106] 1783 = de Polignac prime[366] 1784 = 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[452] 1785 = square pyramidal number,[55] [86] 1786 = centered triangular number [159] 1787 = super-prime , sum of eleven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191)1788 = Euler transform of -1, -2, ..., -34[453] 1789 = number of wiggly sums adding to 17 (terms alternately increase and decrease or vice versa)[454] 1790 = number of partitions of 50 into pairwise relatively prime parts[195] 1791 = largest natural number that cannot be expressed as a sum of at most four hexagonal numbers .1792 = Granville number 1793 = number of lattice points inside a circle of radius 24[154] 1794 = nonagonal number,[214] [72] 1795 = number of heptagons with perimeter 38[455] 1796 = k such that geometric mean of phi(k) and sigma(k) is an integer[330] 1797 = number k such that phi(prime(k)) is a square[327] 1798 = 2 × 29 × 31 = 102 × 111012 × 111112 , which yield zero when the prime factors are xored together[456] 1799 = 2 × 302 − 1 = a twin square [332]
1800 to 1899
1800 = pentagonal pyramidal number,[338] Achilles number , also, in da Ponte's Don Giovanni 1801 = cuban prime , sum of five and nine consecutive primes (349 + 353 + 359 + 367 + 373 and 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227)[412] 1802 = 2 × 302 + 2 = number of points on surface of tetrahedron with edgelength 30,[175] [207] 1803 = number of decahexes that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion)[457] 1804 = number k such that k^64 + 1 is prime 1805 = number of squares between 432 and 434 .[150] 1806 = pronic number,[89] Sylvester's sequence , primary pseudoperfect number ,[458] n equals the denominator of the n th Bernoulli number ,[459] Schröder number [460] 1807 = fifth term of Sylvester's sequence[461] 1808 = maximal number of regions the plane is divided into by drawing 43 circles[239] 1809 = sum of first 17 super-primes [462] 1810 =
∑
k
=
0
4
(
4
k
)
4
{\displaystyle \sum _{k=0}^{4}{\binom {4}{k))^{4))
[463] 1811 = Sophie Germain prime1812 = n such that n32 + 1 is prime[165] 1813 = number of polyominoes with 26 cells, symmetric about two orthogonal axes[464] 1814 = 1 + 6 + 36 + 216 + 1296 + 216 + 36 + 6 + 1 = sum of 4th row of triangle of powers of six[465] 1815 = polygonal chain number
#
(
P
2
,
1
3
)
{\displaystyle \#(P_{2,1}^{3})}
[466] 1816 = number of strict partions of 44[144] 1817 = total number of prime parts in all partitions of 20[467] 1818 = n such that n32 + 1 is prime[165] 1819 = sum of the first 32 primes, minus 32[468] 1820 = pentagonal number,[111] [292] [469] 1821 = member of the Mian–Chowla sequence[56] 1822 = number of integer partitions of 43 whose distinct parts are connected[265] 1823 = super-prime , safe prime[60] 1824 = 432 - 52 , the only way to express 1824 as a difference of prime squares[278] 1825 = octagonal number [182] 1826 = decagonal pyramidal number[295] 1827 = vampire number [238] 1828 = meandric number , open meandric number , appears twice in the first 10 decimal digits of e 1829 = composite de Polignac number [209] 1830 = triangular number1831 = smallest prime with a gap of exactly 16 to next prime (1847)[470] 1832 = sum of totient function for first 77 integers1833 = number of atoms in a decahedron with 13 shells[471] 1834 = octahedral number,[177] 1835 = absolute value of numerator of
D
6
(
5
)
{\displaystyle D_{6}^{(5)))
[472] 1836 = factor by which a proton is more massive than an electron 1837 = star number[124] 1838 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,27}[148] 1839 =
⌊
13
!
3
⌋
{\displaystyle \lfloor {\sqrt[{3}]{13!))\rfloor }
[473] 1840 = 432 - 32 , the only way to express 1840 as a difference of prime squares[278] 1841 = solution to the postage stamp problem with 3 denominations and 29 stamps,[474] 1842 = number of unlabeled rooted trees with 11 nodes[475] 1843 = k such that phi(k) is a perfect cube,[476] 1844 = 37 - 73 ,[477] 1845 = number of partitions of 25 containing at least one prime,[478] 1846 = sum of first 49 composite numbers[213] 1847 = super-prime 1848 = number of edges in the join of two cycle graphs, both of order 42[176] 1849 = 432 , palindromic in base 6 (= 123216 ), centered octagonal number[217] 1850 = Number of partitions of 59 into prime parts 1851 = sum of the first 32 primes1852 = number of quantales on 5 elements, up to isomorphism[479] 1853 = sum of primitive roots of 27-th prime,[480] 1854 = number of permutations of 7 elements with no fixed points,[481] 1855 = rencontres number: number of permutations of [7] with exactly one fixed point[482] 1856 = sum of totient function for first 78 integers1857 = Mertens function zero, pinwheel number[131] 1858 = number of 14-carbon alkanes C14 H30 ignoring stereoisomers[483] 1859 = composite de Polignac number [209] 1860 = number of squares in the Aztec diamond of order 30[484] 1861 = centered square number,[53] 1862 = Mertens function zero, forms a Ruth–Aaron pair with 1863 under second definition1863 = Mertens function zero, forms a Ruth–Aaron pair with 1862 under second definition1864 = Mertens function zero,
1864
!
−
2
2
{\displaystyle {\frac {1864!-2}{2))}
[485] 1865 = 123456 : Largest senary metadrome (number with digits in strict ascending order in base 6)[486] 1866 = Mertens function zero, number of plane partitions of 16 with at most two rows[487] 1867 = prime de Polignac number [366] 1868 = smallest number of complexity 21: smallest number requiring 21 1's to build using +, * and ^[325] 1869 = Hultman number: SH (7, 4)[488] 1870 = decagonal number[135] 1871 = the first prime of the 2 consecutive twin prime pairs: (1871, 1873) and (1877, 1879)[489] 1872 = first Zagreb index of the complete graph K13 [328] 1873 = number of Narayana's cows and calves after 21 years[248] 1874 = area of the 25th conjoined trapezoid [203] 1875 = 502 - 252 1876 = number k such that k^64 + 1 is prime 1877 = number of partitions of 39 where 39 divides the product of the parts[490] 1878 = n such that n32 + 1 is prime[165] 1879 = a prime with square index[491] 1880 = the 10th element of the self convolution of Lucas numbers[492] 1881 = tricapped prism number[493] 1882 = number of linearly separable Boolean functions in 4 variables[494] 1883 = number of conjugacy classes in the alternating group A28 [356] 1884 = k such that 5*2k - 1 is prime[276] 1885 = Zeisel number[316] 1886 = number of partitions of 64 into fourth powers[495] 1887 = number of edges in the hexagonal triangle T(34)[156] 1888 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers )[296] 1889 = Sophie Germain prime, highly cototient number[81] 1890 = triangular matchstick number[86] 1891 = triangular number, hexagonal number,[67] [84] centered triangular number [159] 1892 = pronic number[89] 1893 = 442 - 44 + 1 = H44 (the 44th Hogben number)[199] 1894 = maximal number of regions the plane is divided into by drawing 44 circles[239] 1895 = Stern-Jacobsthal number[283] 1896 = member of the Mian-Chowla sequence[56] 1897 = member of Padovan sequence,[112] [496] 1898 = smallest multiple of n whose digits sum to 26[497] 1899 = cropped hexagone [277]
1900 to 1999
1900 = number of primes <= 214 .[63] 1900 (film)Novecento , 1976 movie. 1900 was the year Thorold Gosset introduced his list of semiregular polytopes ; it is also the year Max Brückner published his study of polyhedral models, including stellations of the icosahedron , such as the novel final stellation of the icosahedron .1901 = Sophie Germain prime, centered decagonal number 1902 = number of symmetric plane partitions of 27[498] 1903 = generalized catalan number[499] 1904 = number of flat partitions of 43[348] 1905 = Fermat pseudoprime [136] 1906 = number n such that 3n - 8 is prime[500] 1907 = safe prime,[60] [132] 1908 = coreful perfect number[342] 1909 = hyperperfect number [501] 1910 = number of compositions of 13 having exactly one fixed point[502] 1911 = heptagonal pyramidal number[185] 1912 = size of 6th maximum raising after one blind in pot-limit poker[503] 1913 = super-prime , Honaker prime[259] 1914 = number of bipartite partitions of 12 white objects and 3 black ones[504] 1915 = number of nonisomorphic semigroups of order 5[505] 1916 = sum of first 50 composite numbers[213] 1917 = number of partitions of 51 into pairwise relatively prime parts[195] 1918 = heptagonal number[106] 1919 = smallest number with reciprocal of period length 36 in base 10[506] 1920 = sum of the nontriangular numbers between successive triangular numbers 1921 = 4-dimensional centered cube number[507] 1922 = Area of a square with diagonal 62[92] 1923 = 2 × 312 + 1 = number of different 2 X 2 determinants with integer entries from 0 to 31[232] 1924 = 2 × 312 + 2 = number of points on surface of tetrahedron with edgelength 31[175] 1925 = number of ways to write 24 as an orderless product of orderless sums[145] 1926 = pentagonal number[111] 1927 = 211 - 112 [508] 1928 = number of distinct values taken by 2^2^...^2 (with 13 2's and parentheses inserted in all possible ways)[509] 1929 = Mertens function zero, number of integer partitions of 42 whose distinct parts are connected[265] 1930 = number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 53[350] 1931 = Sophie Germain prime1932 = number of partitions of 40 into prime power parts[242] 1933 = centered heptagonal number,[107] [259] 1934 = sum of totient function for first 79 integers1935 = number of edges in the join of two cycle graphs, both of order 43[176] 1936 = 442 , 18-gonal number,[510] 1937 = number of chiral n-ominoes in 12-space, one cell labeled[511] 1938 = Mertens function zero, number of points on surface of octahedron with edgelength 22[180] 1939 = 7-Knödel number[164] 1940 = the Mahonian number: T(8, 9)[222] 1941 = maximal number of regions obtained by joining 16 points around a circle by straight lines[512] 1942 = number k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes[513] 1943 = largest number not the sum of distinct tetradecagonal numbers[514] 1944 = 3-smooth number (23 ×35 ), Achilles number [377] 1945 = number of partitions of 25 into relatively prime parts such that multiplicities of parts are also relatively prime[515] 1946 = number of surface points on a cube with edge-length 19[57] 1947 = k such that 5·2k + 1 is a prime factor of a Fermat number 22m + 1 for some m[516] 1948 = number of strict solid partitions of 20[127] 1949 = smallest prime > 442 .[183] 1950 =
1
⋅
2
⋅
3
+
4
⋅
5
⋅
6
+
7
⋅
8
⋅
9
+
10
⋅
11
⋅
12
{\displaystyle 1\cdot 2\cdot 3+4\cdot 5\cdot 6+7\cdot 8\cdot 9+10\cdot 11\cdot 12}
[517] [514] 1951 = cuban prime[412] 1952 = number of covers of {1, 2, 3, 4}[518] 1953 = triangular number1954 = number of sum-free subsets of {1, ..., 16}[307] 1955 = number of partitions of 25 with at least one distinct part[233] 1956 = nonagonal number[214] 1957 =
∑
k
=
0
6
6
!
k
!
{\displaystyle \sum _{k=0}^{6}{\frac {6!}{k!))}
[519] 1958 = number of partitions of 25[235] 1959 = Heptanacci-Lucas number[520] 1960 = number of parts in all partitions of 33 into distinct parts[83] 1961 = number of lattice points inside a circle of radius 25[154] 1962 = number of edges in the join of the complete graph K36 and the cycle graph C36 [521] 1963 ! - 1 is prime[522] 1964 = number of linear forests of planted planar trees with 8 nodes[523] 1965 = total number of parts in all partitions of 17[103] 1966 = sum of totient function for first 80 integers1967 = least edge-length of a square dissectable into at least 30 squares in the Mrs. Perkins's quilt problem[524] σ(1968) = σ(1967) + σ(1966)[525] 1969 = Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize[526] 1970 = number of compositions of two types of 9 having no even parts[527] 1971 =
3
7
−
6
3
{\displaystyle 3^{7}-6^{3))
[528] 1972 = n such that
n
37
−
1
n
−
1
{\displaystyle {\frac {n^{37}-1}{n-1))}
[529] 1973 = Sophie Germain prime, Leonardo prime 1974 = number of binary vectors of length 17 containing no singletons[215] 1975 = number of partitions of 28 with nonnegative rank[389] 1976 = octagonal number [182] 1977 = number of non-isomorphic multiset partitions of weight 9 with no singletons[530] 1978 = n such that n | (3n + 5)[531] 1979 = number of squares between 452 and 454 .[150] 1980 = pronic number[89] 1981 = pinwheel number[131] 1982 = maximal number of regions the plane is divided into by drawing 45 circles[239] 1983 = skiponacci number[155] 1984 = 11111000000 in binary , see also: 1984 (disambiguation) 1985 = centered square number [53] 1986 = number of ways to write 25 as an orderless product of orderless sums[145] 1987 prime number 1988 = sum of the first 33 primes1989 = number of 9-step mappings with 4 inputs[297] 1990 = Stella octangula number 1991 = 11 × 181, the 46th Gullwing number,[532] [533] 1992 = number of nonisomorphic sets of nonempty subsets of a 4-set[534] 1993 = a number with the property that 41993 - 31993 is prime,[535] [146] 1994 = Glaisher's function W(37)[536] 1995 = number of unlabeled graphs on 9 vertices with independence number 6[537] 1996 = a number with the property that (1996! + 3)/3 is prime[538] 1997 =
∑
k
=
1
21
k
⋅
ϕ
(
k
)
{\displaystyle \sum _{k=1}^{21}{k\cdot \phi (k)))
[539] 1998 = triangular matchstick number[86] 1999 = centered triangular number [540] regular forms in a myriagram .
Prime numbers
There are 135 prime numbers between 1000 and 2000:[541] [542]
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 
![{\displaystyle \lfloor {\sqrt[{3}]{13!))\rfloor }](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f0943f39851d7f678812a33ee092226567c63e4)
