XIV

1000/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. A period of one thousand years may be known as a chiliad or, more often from 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.

Notation※

• The decimal representation for one thousand is
  • 1000—a one followed by, three zeros, in the general notation;
  • 1 × 10—in engineering notation, which for this number coincides with:
  • 1 × 10 exactly—in scientific normalized exponential notation;
  • 1 E+3 exactly—in scientific E notation.
• The SI prefix for a thousand units is "kilo-", abbreviated——to "k"—for instance, a kilogram or "kg" is a thousand grams. This is sometimes extended to non-SI contexts, such as "ka" (kiloannum) being used as a shorthand for periods of 1000 years. In computer science, however, "kilo-" is used more loosely to mean 2 to the 10th power (1024).
• In the SI writing style, a non-breaking space can be used as a thousands separator, i.e., to separate the "digits of a number at every power of 1000."
• Multiples of thousands are occasionally represented by replacing their last three zeros with the letter "K" or "k": for instance, writing "$30k" for $30 000 or denoting the Y2K computer bug of the year 2000.
• A thousand units of currency, especially dollars or pounds, are colloquially called a grand. In the United States, this is sometimes abbreviated with a "G" suffix.

Properties※

1000 is the 10th icositetragonal number, or 24-gonal number. It is also the 16th generalized 30-gonal number.

1000 is the Wiener index of cycle length 20, also the sum of labeled boxes arranged as a pyramid with base 1 – 20.

1000 is the element of multiplicity in a ${\displaystyle 24\times 24}$ toroidal board in the n-Queens problem, with respective indicator of 25 and count of 51.

1000 is the number of strict partitions of 50 containing the sum of no subset of the parts.

A chiliagon is a 1000-sided polygon, of order 2000 in its regular form.

Totient values※

1000 has a reduced totient value ${\displaystyle \lambda (n)}$ of 100, and Euler totient ${\displaystyle \varphi (n)}$ of 400.

11 integers have a totient value of 1000 (1111, 1255, ..., 3750).

One thousand is also equal to the sum of Euler's totient summatory function ${\displaystyle \Phi (n)}$ over the first 57 integers.

Repdigits※

In decimal, multiples of one thousand are totient values of four-digit repdigits:

In the list of composite numbers, 7777 is very nearly the composite index of 8888: 8886 is the 7779th composite number. Also,

1600 = 40 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 10.

The sum of the first nine prime numbers up to 23 is 100, with ${\displaystyle \varphi (p(23))=1000}$, where ${\displaystyle p(23)=1255}$ is the number of integer partitions of 23.

Prime values※

Using decimal representation as well,

On the other hand, the largest prime number less than 10000 is the 1229th prime number, 9973.

1000 is also the smallest number in base-ten that generates three primes in the fastest way possible by concatenation with decremented numbers:

all represent prime numbers.

Adding the prime 853 with its prime index of 147 yields 1000.

Sporadic groups※

The one-thousandth prime number is 7919. It is a difference of 1 from the order of the smallest sporadic group: ${\displaystyle |\mathrm {M} _{11}|=7920}$.

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 22

1003 = the product of some prime p and the p prime, namely p = 17.

1004 = heptanacci number

1005 = Mertens function zero, decagonal pyramidal number

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; record gap between twin primes; number that is the sum of 7 positive 5th powers. In decimal: 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 = 0, 1 = 1, 8 = 2, 216 = 6)

1007 = number that is the sum of 8 positive 5th powers

1008 = divisible by the number of primes below it

1009 = 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 = 10 + 10, Mertens function zero

1011 = the largest n such that 2 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

1012 = ternary number, (32₁₀) quadruple triangular number (triangular number is 253), number of partitions of 1 into reciprocals of positive integers <= 17 Egyptian fraction

1013 = Sophie Germain prime, centered square number, Mertens function zero

1014 = 2-10, Mertens function zero, sum of the nontriangular numbers between successive triangular numbers 78 and 91

1015 = square pyramidal number

1016 = member of the Mian–Chowla sequence, stella octangula number, number of surface points on a cube with edge-length 14

1017 = generalized triacontagonal number

1018 = Mertens function zero, 1018 + 1 is prime

1019 = Sophie Germain prime, safe prime, Chen prime

1020 = polydivisible number

1021 = twin prime with 1019. It is also a Lucky prime.

1022 = Friedman number

1023 = sum of five consecutive primes (193 + 197 + 199 + 211 + 223); the number of three-dimensional polycubes with 7 cells; 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 = 32 = 4 = 2, 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 2 + 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 (4 + 4); 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 <= 2.

1029 = can be written from base 2 to base 18 using only the digits 0 to 9.

1030 = generalized heptagonal number

1031 = exponent and number of ones for the fifth base-10 repunit prime, Sophie Germain prime, 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

1035 = triangular number, hexagonal number

1036 = central polygonal number

1037 = number in E-toothpick sequence

1038 = even integer that is an unordered sum of two primes in exactly n ways

1039 = prime of the form 8n+7, number of partitions of 30 that do not contain 1 as a part, Chen prime

1040 = 4 + 4: sum of distinct powers of 4. The number of pieces that could be seen in a 6 × 6 × 6× 6 Rubik's Tesseract.

1041 = sum of 11 positive 5th powers

1042 = sum of 12 positive 5th powers

1043 = number whose sum of even digits and sum of odd digits are even

1044 = sum of distinct powers of 4

1045 = octagonal number

1046 = coefficient of f(q) (3rd order mock theta function)

1047 = number of ways to split a strict composition of 18 into contiguous subsequences that have the same sum

1048 = number of partitions of 27 into squarefree parts

1049 = Sophie Germain prime, highly cototient number, Chen prime

1050 = 1050₈ to decimal becomes a pronic number (552₁₀), number of parts in all partitions of 29 into distinct parts

1051 = centered pentagonal number, centered decagonal number

1052 = sum of 9 positive 6th powers

1053 = triangular matchstick number

1054 = centered triangular number

1055 = sum of 12 positive 6th powers

1056 = pronic number

1057 = central polygonal number

1058 = sum of 4 positive 5th powers, area of a square with diagonal 46

1059 = number n such that n is written in the form of a sum of four positive 4th powers

1060 = sum of the first 25 primes from 2 through 97 (the number of primes less than 100), and sixth sum of 10 consecutive primes, starting with 23 through 131.

1061 = emirp, twin prime with 1063, number of prime numbers between 1000 and 10000 (or, number of four-digit primes in decimal representation)

1062 = number that is not the sum of two palindromes

1063 = super-prime, sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167); near-wall-sun-sun prime

1064 = sum of two positive cubes

1065 = generalized duodecagonal

1066 = number whose sum of their divisors is a square

1067 = number of strict integer partitions of 45 in which are empty or have smallest part not dividing the other ones

1068 = number that is the sum of 7 positive 5th powers, total number of parts in all partitions of 15

1069 = emirp

1070 = number that is the sum of 9 positive 5th powers

1071 = heptagonal number

1072 = centered heptagonal number

1073 = number that is the sum of 12 positive 5th powers

1074 = number that is not the sum of two palindromes

1075 = number non-sum of two palindromes

1076 = number of strict trees weight 11

1077 = number where 7 outnumbers every other digit in the number

1078 = Euler transform of negative integers

1079 = every positive integer is the sum of at most 1079 tenth powers.

1080 = pentagonal number

1081 = triangular number, member of Padovan sequence

1082 = central polygonal number

1083 = three-quarter square, number of partitions of 53 into prime parts

1084 = third spoke of a hexagonal spiral, 1084 + 1 is prime

1085 = number of partitions of n into distinct parts > or = 2

1086 = Smith number, sum of totient function for first 59 integers

1087 = super-prime, cousin prime, lucky prime

1088 = octo-triangular number, (triangular number result being 136) sum of two distinct powers of 2, (1024 + 64) number that is divisible by exactly seven primes with the inclusion of multiplicity

1089 = 33, nonagonal number, centered octagonal number, first natural number whose digits in its decimal representation get reversed when multiplied by 9.

1090 = sum of 5 positive 5th powers

1091 = cousin prime and twin prime with 1093

1092 = divisible by the number of primes below it

1093 = the smallest Wieferich prime (the only other known Wieferich prime is 3511), twin prime with 1091 and star number

1094 = sum of 9 positive 5th powers, 1094 + 1 is prime

1095 = sum of 10 positive 5th powers, number that is not the sum of two palindromes

1096 = hendecagonal number, number of strict solid partitions of 18

1097 = emirp, Chen prime

1098 = multiple of 9 containing digit 9 in its base-10 representation

1099 = number where 9 outnumbers every other digit

1100 to 1199※

1100 = number of partitions of 61 into distinct squarefree parts

1101 = pinwheel number

1102 = sum of totient function for first 60 integers

1103 = Sophie Germain prime, balanced prime

1104 = Keith number

1105 = 33 + 4 = 32 + 9 = 31 + 12 = 23 + 24, Carmichael number, magic constant of n × n normal magic square and n-queens problem for n = 13, decagonal number, centered square number, Fermat pseudoprime

1106 = number of regions into which the plane is divided when drawing 24 ellipses

1107 = number of non-isomorphic strict T₀ multiset partitions of weight 8

1108 = number k such that k + 1 is prime

1109 = Friedlander-Iwaniec prime, Chen prime

1110 = k such that 2 + 3 is prime

1111 = 11 × 101, palindrome that is a product of two palindromic primes, repunit

1112 = k such that 9 - 2 is a prime

1113 = number of strict partions of 40

1114 = number of ways to write 22 as an orderless product of orderless sums

1115 = number of partitions of 27 into a prime number of parts

1116 = divisible by the number of primes below it

1117 = number of diagonally symmetric polyominoes with 16 cells, Chen prime

1118 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,21}

1119 = number of bipartite graphs with 9 nodes

1120 = number k such that k + 1 is prime

1121 = number of squares between 34 and 34.

1122 = pronic number, divisible by the number of primes below it

1123 = balanced prime

1124 = Leyland number = 2 + 10, spy number

1125 = Achilles number

1126 = number of 2 × 2 non-singular integer matrices with entries from {0, 1, 2, 3, 4, 5}

1127 = maximal number of pieces that can be obtained by cutting an annulus with 46 cuts

1128 = 47th triangular number, 24th hexagonal number, divisible by the number of primes below it (188 × 6). 1128 is the dimensional representation of the largest vertex operator algebra with central charge of 24, D₂₄.

1129 = number of lattice points inside a circle of radius 19

1130 = skiponacci number

1131 = number of edges in the hexagonal triangle T(26)

1132 = number of simple unlabeled graphs with 9 nodes of 2 colors whose components are complete graphs

1133 = number of primitive subsequences of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

1134 = divisible by the number of primes below it, triangular matchstick number

1135 = centered triangular number

1136 = number of independent vertex sets and vertex covers in the 7-sunlet graph

1137 = sum of values of vertices at level 5 of the hyperbolic Pascal pyramid

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)

1140 = tetrahedral number

1141 = 7-Knödel number

1142 = n such that n + 1 is prime, spy number

1143 = number of set partitions of 8 elements with 2 connectors

1144 is not the sum of a pair of twin primes

1145 = 5-Knödel number

1146 is not the sum of a pair of twin primes

1147 = 31 × 37 (a product of 2 successive primes)

1148 is not the sum of a pair of twin primes

1149 = a product of two palindromic primes

1150 = number of 11-iamonds without bilateral symmetry.

1151 = first prime following prime gap of 22, Chen prime

1152 = highly totient number, 3-smooth number (2×3), area of a square with diagonal 48, Achilles number

1153 = super-prime, Proth prime

1154 = 2 × 24 + 2 = number of points on surface of tetrahedron with edgelength 24

1155 = number of edges in the join of two cycle graphs, both of order 33

1156 = 34, octahedral number, centered pentagonal number, centered hendecagonal number.

1157 = smallest number that can be written as n^2+1 without any prime factors that can be written as a^2+1.

1158 = number of points on surface of octahedron with edgelength 17

1159 = member of the Mian–Chowla sequence, a centered octahedral number

1160 = octagonal number

1161 = sum of the first 26 primes

1162 = pentagonal number, sum of totient function for first 61 integers

1163 = smallest prime > 34. See 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

1165 = 5-Knödel number

1166 = heptagonal pyramidal number

1167 = number of rational numbers which can be constructed from the set of integers between 1 and 43

1168 = antisigma(49)

1169 = highly cototient number

1170 = highest possible score in a National Academic Quiz Tournaments (NAQT) match

1171 = super-prime

1172 = number of subsets of first 14 integers that have a sum divisible by 14

1173 = number of simple triangulation on a plane with 9 nodes

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

1176 = triangular number

1177 = heptagonal number

1178 = number of surface points on a cube with edge-length 15

1179 = number of different permanents of binary 7*7 matrices

1180 = smallest number of non-integral partitions into non-integral power >1000.

1181 = smallest k over 1000 such that 8*10^k-49 is prime.

1182 = number of necklaces possible with 14 beads of 2 colors (that cannot be turned over)

1183 = pentagonal pyramidal number

1184 = amicable number with 1210

1185 = number of partitions of 45 into pairwise relatively prime parts

1186 = number of diagonally symmetric polyominoes with 15 cells, number of partitions of 54 into prime parts

1187 = safe prime, Stern prime, balanced prime, Chen prime

1188 = first 4 digit multiple of 18 to contain 18

1189 = number of squares between 35 and 35.

1190 = pronic number, number of cards to build an 28-tier house of cards

1191 = 35 - 35 + 1 = H₃₅ (the 35th Hogben number)

1192 = sum of totient function for first 62 integers

1193 = a number such that 4 - 3 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

1195 = smallest four digit number for which a(n) is an integer is a(n) is 2*a(n-1) - (-1)

1196 = ${\displaystyle \sum _{k=1}^{38}\sigma (k)}$

1197 = pinwheel number

1198 = centered heptagonal number

1199 = area of the 20th conjoined trapezoid

1200 to 1299※

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, number k such that k + 1 is prime

1201 = centered square number, super-prime, centered decagonal number

1202 = number of regions the plane is divided into by 25 ellipses

1203: first 4 digit number in the coordinating sequence for the (2,6,∞) tiling of the hyperbolic plane

1204: magic constant of a 7 × 7 × 7 magic cube

1205 = number of partitions of 28 such that the number of odd parts is a part

1206 = 29-gonal number

1207 = composite de Polignac number

1208 = number of strict chains of divisors starting with the superprimorial A006939(3)

1209 = The product of all ordered non-empty subsets of {3,1} if {a,b} is a||b: 1209=1*3*13*31

1210 = amicable number with 1184

1211 = composite de Polignac number

1212 = ${\displaystyle \sum _{k=0}^{17}p(k)}$, where ${\displaystyle p}$ is the number of partions of ${\displaystyle k}$

1213 = emirp

1214 = sum of first 39 composite numbers, spy number

1215 = number of edges in the hexagonal triangle T(27)

1216 = nonagonal number

1217 = super-prime, Proth prime

1218 = triangular matchstick number

1219 = Mertens function zero, centered triangular number

1220 = Mertens function zero, number of binary vectors of length 16 containing no singletons

1221 = product of the first two digit, and three digit repdigit

1222 = hexagonal pyramidal number

1223 = Sophie Germain prime, balanced prime, 200th prime number

1224 = number of edges in the join of two cycle graphs, both of order 34

1225 = 35, square triangular number, hexagonal number, centered octagonal number, icosienneagonal, hexacontagonal and hecatonicositetragonal (124-gonal). Sum of 5 consecutive odd cubes (1³ + 3³ + 5³ + 7³ + 9³)

1226 = number of rooted identity trees with 15 nodes

1227 = smallest number representable as the sum of 3 triangular numbers in 27 ways

1228 = sum of totient function for first 63 integers

1229 = Sophie Germain prime, number of primes between 0 and 10000, emirp

1230 = the Mahonian number: T(9, 6)

1231 = smallest mountain emirp, as 121, smallest mountain number is 11 × 11

1232 = number of labeled ordered set of partitions of a 7-set into odd parts

1233 = 12 + 33

1234 = number of parts in all partitions of 30 into distinct parts, smallest whole number containing all numbers from 1 to 4

1235 = excluding duplicates, contains the first four Fibonacci numbers

1236 = 617 + 619: sum of twin prime pair

1237 = prime of the form 2p-1

1238 = number of partitions of 31 that do not contain 1 as a part

1239 = toothpick number in 3D

1240 = square pyramidal number

1241 = centered cube number, spy number

1242 = decagonal number

1243 = composite de Polignac number

1244 = number of complete partitions of 25

1245 = Number of labeled spanning intersecting set-systems on 5 vertices.

1246 = number of partitions of 38 such that no part occurs more than once

1247 = pentagonal number

1248 = the first four powers of 2 concatenated together

1249 = emirp, trimorphic number

1250 = area of a square with diagonal 50

1251 = 2 × 25 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 25

1252 = 2 × 25 + 2 = number of points on surface of tetrahedron with edgelength 25

1253 = number of partitions of 23 with at least one distinct part

1254 = number of partitions of 23 into relatively prime parts

1255 = Mertens function zero, number of ways to write 23 as an orderless product of orderless sums, number of partitions of 23

1256 = 1 × 2 × (5) + 6, Mertens function zero

1257 = number of lattice points inside a circle of radius 20

1258 = 1 × 2 × (5) + 8, Mertens function zero

1259 = highly cototient number

1260 = highly composite number, pronic number, the smallest vampire number, sum of totient function for first 64 integers, number of strict partions of 41 and appears twice in the Book of Revelation

1261 = star number, Mertens function zero

1262 = maximal number of regions the plane is divided into by drawing 36 circles

1263 = rounded total surface area of a regular tetrahedron with edge length 27

1264 = sum of the first 27 primes

1265 = number of rooted trees with 43 vertices in which vertices at the same level have the same degree

1266 = centered pentagonal number, Mertens function zero

1267 = 7-Knödel number

1268 = number of partitions of 37 into prime power parts

1269 = least number of triangles of the Spiral of Theodorus to complete 11 revolutions

1270 = 25 + 24×26 + 23×27, Mertens function zero

1271 = sum of first 40 composite numbers

1272 = sum of first 41 nonprimes

1273 = 19 × 67 = 19 × prime(19)

1274 = sum of the nontriangular numbers between successive triangular numbers

1275 = triangular number, sum of the first 50 natural numbers

1276 = number of irredundant sets in the 25-cocktail party graph

1277 = the start of a prime constellation of length 9 (a "prime nonuple")

1278 = number of Narayana's cows and calves after 20 years

1279 = Mertens function zero, Mersenne prime exponent

1280 = Mertens function zero, number of parts in all compositions of 9

1281 = octagonal number

1282 = Mertens function zero, number of partitions of 46 into pairwise relatively prime parts

1283 = safe prime

1284 = 641 + 643: sum of twin prime pair

1285 = Mertens function zero, number of free nonominoes, number of parallelogram polyominoes with 10 cells.

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

1287 = ${\displaystyle {13 \choose 5}}$

1288 = heptagonal number

1289 = Sophie Germain prime, Mertens function zero

1290 = ${\displaystyle {\frac {1289+1291}{2}}}$, average of a twin prime pair

1291 = largest prime < 6, Mertens function zero

1292 = number such that phi(1292) = phi(sigma(1292)), Mertens function zero

1293 = ${\displaystyle \sum _{j=1}^{n}j\times prime(j)}$

1294 = rounded volume of a regular octahedron with edge length 14

1295 = number of edges in the join of two cycle graphs, both of order 35

1296 = 36 = 6, 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

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

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 number

1301 = centered square number, Honaker prime, number of trees with 13 unlabeled nodes

1302 = Mertens function zero, number of edges in the hexagonal triangle T(28)

1303 = prime of form 21n+1 and 31n+1

1304 = sum of 1304₆ and 1304 ₉ which is 328+976

1305 = triangular matchstick number

1306 = Mertens function zero. In base 10, raising the digits of 1306 to powers of successive integers equals itself: 1306 = 1 + 3 + 0 + 6. 135, 175, 518, and 598 also have this property. Centered triangular number.

1307 = safe prime

1308 = sum of totient function for first 65 integers

1309 = the first sphenic number followed by two consecutive such number

1310 = smallest number in the middle of a set of three sphenic numbers

1311 = number of integer partitions of 32 with no part dividing all the others

1312 = member of the Mian-Chowla sequence;

1313 = sum of all parts of all partitions of 14

1314 = number of integer partitions of 41 whose distinct parts are connected

1315 = 10^(2n+1)-7*10^n-1 is prime.

1316 = Euler transformation of sigma(11)

1317 = 1317 Only odd four digit number to divide the concatenation of all number up to itself in base 25

1318 + 1 is prime, Mertens function zero

1319 = safe prime

1320 = 659 + 661: sum of twin prime pair

1321 = Friedlander-Iwaniec prime

1322 = area of the 21st conjoined trapezoid

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))

1325 = Markov number, centered tetrahedral number

1326 = triangular number, hexagonal number, Mertens function zero

1327 = first prime followed by 33 consecutive composite numbers

1328 = sum of totient function for first 66 integers

1329 = Mertens function zero, sum of first 41 composite numbers

1330 = tetrahedral number, forms a Ruth–Aaron pair with 1331 under second definition

1331 = 11, centered heptagonal number, forms a Ruth–Aaron pair with 1330 under second definition. This is the only non-trivial cube of the form x + x − 1, for x = 36.

1332 = pronic number

1333 = 37 - 37 + 1 = H₃₇ (the 37th Hogben number)

1334 = maximal number of regions the plane is divided into by drawing 37 circles

1335 = pentagonal number, Mertens function zero

1336 = sum of gcd(x, y) for 1 <= x, y <= 24, Mertens function zero

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, Mertens function zero

1339 = First 4 digit number to appear twice in the sequence of sum of cubes of primes dividing n

1340 = k such that 5 × 2 - 1 is prime

1341 = First mountain number with 2 jumps of more than one.

1342 = ${\displaystyle \sum _{k=1}^{40}\sigma (k)}$, Mertens function zero

1343 = cropped hexagone

1344 = 37 - 5, the only way to express 1344 as a difference of prime squares

1345 = k such that k, k+1 and k+2 are products of two primes

1346 = number of locally disjointed rooted trees with 10 nodes

1347 = concatenation of first 4 Lucas numbers

1348 = number of ways to stack 22 pennies such that every penny is in a stack of one or two

1349 = Stern-Jacobsthal number

1350 = nonagonal number

1351 = number of partitions of 28 into a prime number of parts

1352 = number of surface points on a cube with edge-length 16, Achilles number

1353 = 2 × 26 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 26

1354 = 2 × 26 + 2 = number of points on surface of tetrahedron with edgelength 26

1355 appears for the first time in the Recamán's sequence at n = 325,374,625,245. Or in other words A057167(1355) = 325,374,625,245

1356 is not the sum of a pair of twin primes

1357 = number of nonnegative solutions to x + y ≤ 41

1358 = rounded total surface area of a regular tetrahedron with edge length 28

1359 is the 42d term of Flavius Josephus's sieve

1360 = 37 - 3, the only way to express 1360 as a difference of prime squares

1361 = first prime following prime gap of 34, centered decagonal number, 3rd Mills' prime, Honaker prime

1362 = number of achiral integer partitions of 48

1363 = the number of ways to modify a circular arrangement of 14 objects by swapping one or more adjacent pairs

1364 = Lucas number

1365 = pentatope number

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

1367 = safe prime, 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),

1368 = number of edges in the join of two cycle graphs, both of order 36

1369 = 37, centered octagonal number

1370 = σ₂(37): sum of squares of divisors of 37

1371 = sum of the first 28 primes

1372 = Achilles number

1373 = number of lattice points inside a circle of radius 21

1374 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,23}

1375 = decagonal pyramidal number

1376 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)

1377 = maximal number of pieces that can be obtained by cutting an annulus with 51 cuts

1378 = triangular number

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

1381 = centered pentagonal number Mertens function zero

1382 = first 4 digit tetrachi number

1383 = 3 × 461. 10 + 7 is prime

1384 = ${\displaystyle \sum _{k=1}^{41}\sigma (k)}$

1385 = up/down number

1386 = octagonal pyramidal number

1387 = 5th Fermat pseudoprime of base 2, 22nd centered hexagonal number and the 19th decagonal number, second Super-Poulet number.

1388 = 4 × 19 - 3 × 19 + 1 and is therefore on the x-axis of Ulams spiral

1389 = sum of first 42 composite numbers

1390 = sum of first 43 nonprimes

1391 = number of rational numbers which can be constructed from the set of integers between 1 and 47

1392 = number of edges in the hexagonal triangle T(29)

1393 = 7-Knödel number

1394 = sum of totient function for first 67 integers

1395 = vampire number, member of the Mian–Chowla sequence triangular matchstick number

1396 = centered triangular number

1397 = ${\displaystyle \left\lfloor 5^{\frac {9}{2}}\right\rfloor }$

1398 = number of integer partitions of 40 whose distinct parts are connected

1399 = emirp

1400 to 1499※

1400 = number of sum-free subsets of {1, ..., 15}

1401 = pinwheel number

1402 = number of integer partitions of 48 whose augmented differences are distinct, number of signed trees with 8 nodes

1403 = smallest x such that M(x) = 11, where M() is Mertens function

1404 = heptagonal number

1405 = 26 + 27, 7 + 8 + ... + 16, centered square number

1406 = pronic number, semi-meandric number

1407 = 38 - 38 + 1 = H₃₈ (the 38th Hogben number)

1408 = maximal number of regions the plane is divided into by drawing 38 circles

1409 = super-prime, Sophie Germain prime, smallest number whose eighth power is the sum of 8 eighth powers, Proth prime

1410 = denominator of the 46th Bernoulli number

1411 = LS(41)

1412 = LS(42), spy number

1413 = LS(43)

1414 = smallest composite that when added to sum of prime factors reaches a prime after 27 iterations

1415 = the Mahonian number: T(8, 8)

1416 = LS(46)

1417 = number of partitions of 32 in which the number of parts divides 32

1418 = smallest x such that M(x) = 13, where M() is Mertens function

1419 = Zeisel number

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, spy number

1422 = number of partitions of 15 with two parts marked

1423 = 200 + 1223 and the 200th prime is 1223 Also Used as a Hate symbol

1424 = number of nonnegative solutions to x + y ≤ 42

1425 = self-descriptive number in base 5

1426 = sum of totient function for first 68 integers, pentagonal number, number of strict partions of 42

1427 = twin prime together with 1429

1428 = number of complete ternary trees with 6 internal nodes, or 18 edges

1429 = number of partitions of 53 such that the smallest part is greater than or equal to number of parts

1430 = Catalan number

1431 = triangular number, hexagonal number

1432 = member of Padovan sequence

1433 = super-prime, Honaker prime, typical port used for remote connections to Microsoft SQL Server databases

1434 = rounded volume of a regular tetrahedron with edge length 23

1435 = vampire number; the standard railway gauge in millimetres, equivalent to 4 feet 8+1⁄2 inches (1.435 m)

1436 = discriminant of a totally real cubic field

1437 = smallest number of complexity 20: smallest number requiring 20 1's to build using +, * and ^

1438 = k such that 5 × 2 - 1 is prime

1439 = Sophie Germain prime, safe prime

1440 = a highly totient number and a 481-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 displays

1441 = star number

1442 = number of parts in all partitions of 31 into distinct parts

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

1444 = 38, smallest pandigital number in Roman numerals

1445 = ${\displaystyle \sum _{k=0}^{3}\left({\binom {3}{k}}\times {\binom {3+k}{k}}\right)^{2}}$

1446 = number of points on surface of octahedron with edgelength 19

1447 = super-prime, happy number

1448 = number k such that phi(prime(k)) is a square

1449 = Stella octangula number

1450 = σ₂(34): sum of squares of divisors of 34

1451 = Sophie Germain prime

1452 = first Zagreb index of the complete graph K₁₂

1453 = Sexy prime with 1459

1454 = 3 × 22 + 2 = number of points on surface of square pyramid of side-length 22

1455 = k such that geometric mean of phi(k) and sigma(k) is an integer

1456 = number of regions in regular 15-gon with all diagonals drawn

1457 = 2 × 27 − 1 = a twin square

1458 = maximum determinant of an 11 by 11 matrix of zeroes and ones, 3-smooth number (2×3)

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

1462 = (35 - 1) × (35 + 8) = the first Zagreb index of the wheel graph with 35 vertices

1463 = total number of parts in all partitions of 16

1464 = rounded total surface area of a regular icosahedron with edge length 13

1465 = 5-Knödel number

1466 = ${\displaystyle \sum _{k=1}^{256}d(k)}$, where ${\displaystyle d(k)}$ = number of divisors of ${\displaystyle k}$

1467 = number of partitions of 39 with zero crank

1468 = number of polyhexes with 11 cells that tile the plane by translation

1469 = octahedral number, highly cototient number

1470 = pentagonal pyramidal number, sum of totient function for first 69 integers

1471 = super-prime, centered heptagonal number

1472 = number of overpartitions of 15

1473 = cropped hexagone

1474 = ${\displaystyle {\frac {44(44+1)}{2}}+{\frac {44^{2}}{4}}}$: triangular number plus quarter square (i.e., A000217(44) + A002620(44))

1475 = number of partitions of 33 into parts each of which is used a different number of times

1476 = coreful perfect number

1477 = 7-Knödel number

1478 = total number of largest parts in all compositions of 11

1479 = number of planar partitions of 12

1480 = sum of the first 29 primes

1481 = Sophie Germain prime

1482 = pronic number, number of unimodal compositions of 15 where the maximal part appears once

1483 = 39 - 39 + 1 = H₃₉ (the 39th Hogben number)

1484 = maximal number of regions the plane is divided into by drawing 39 circles

1485 = triangular number

1486 = number of strict solid partitions of 19

1487 = safe prime

1488 = triangular matchstick number

1489 = centered triangular number

1490 = tetranacci number

1491 = nonagonal number, Mertens function zero

1492 = discriminant of a totally real cubic field, Mertens function zero

1493 = Stern prime

1494 = sum of totient function for first 70 integers

1495 = 9###

1496 = square pyramidal number

1497 = skiponacci number

1498 = number of flat partitions of 41

1499 = Sophie Germain prime, super-prime

1500 to 1599※

1500 = hypotenuse in three different Pythagorean triangles

1501 = centered pentagonal number

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

1503 = least number of triangles of the Spiral of Theodorus to complete 12 revolutions

1504 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)

1505 = number of integer partitions of 41 with distinct differences between successive parts

1506 = number of Golomb partitions of 28

1507 = number of partitions of 32 that do not contain 1 as a part

1508 = heptagonal pyramidal number

1509 = pinwheel number

1510 = deficient number, odious number

1511 = Sophie Germain prime, balanced prime

1512 = k such that geometric mean of phi(k) and sigma(k) is an integer

1513 = centered square number

1514 = sum of first 44 composite numbers

1515 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 30-manifold to be realizable as a sub-manifold

1516 = ${\displaystyle \left\lfloor 9^{\frac {10}{3}}\right\rfloor }$

1517 = number of lattice points inside a circle of radius 22

1518 = sum of first 32 semiprimes, Mertens function zero

1519 = number of polyhexes with 8 cells, Mertens function zero

1520 = pentagonal number, Mertens function zero, forms a Ruth–Aaron pair with 1521 under second definition

1521 = 39, Mertens function zero, centered octagonal number, forms a Ruth–Aaron pair with 1520 under second definition

1522 = k such that 5 × 2 - 1 is prime

1523 = super-prime, Mertens function zero, safe prime, member of the Mian–Chowla sequence

1524 = Mertens function zero, k such that geometric mean of phi(k) and sigma(k) is an integer

1525 = heptagonal number, Mertens function zero

1526 = number of conjugacy classes in the alternating group A₂₇

1527 = number of 2-dimensional partitions of 11, Mertens function zero

1528 = Mertens function zero, rounded total surface area of a regular octahedron with edge length 21

1529 = composite de Polignac number

1530 = vampire number

1531 = prime number, centered decagonal number, Mertens function zero

1532 = number of series-parallel networks with 9 unlabeled edges, Mertens function zero

1533 = 21 × 73 = 21 × 21st prime

1534 = number of achiral integer partitions of 50

1535 = Thabit number

1536 = a common size of microplate, 3-smooth number (2×3), number of threshold functions of exactly 4 variables

1537 = Keith number, Mertens function zero

1538 = number of surface points on a cube with edge-length 17

1539 = maximal number of pieces that can be obtained by cutting an annulus with 54 cuts

1540 = triangular number, hexagonal number, decagonal number, tetrahedral number

1541 = octagonal number

1542 = k such that 2^k starts with k

1543 = prime dividing all Fibonacci sequences, Mertens function zero

1544 = Mertens function zero, number of partitions of integer partitions of 17 where all parts have the same length

1545 = number of reversible string structures with 9 beads using exactly three different colors

1546 = number of 5 X 5 binary matrices with at most one 1 in each row and column, Mertens function zero

1547 = hexagonal pyramidal number

1548 = coreful perfect number

1549 = de Polignac prime

1550 = ${\displaystyle {\frac {31\times (3\times 31+7)}{2}}}$ = number of cards needed to build a 31-tier house of cards with a flat, one-card-wide roof

1551 = 6920 - 5369 = A169952(24) - A169952(23) = A169942(24) = number of Golomb rulers of length 24

1552 = Number of partitions of 57 into prime parts

1553 = 509 + 521 + 523 = a prime that is the sum of three consecutive primes

1554 = 2 × 3 × 7 × 37 = product of four distinct primes

1555 divides 6

1556 = sum of the squares of the first nine primes

1557 = number of graphs with 8 nodes and 13 edges

1558 = number k such that k + 1 is prime

1559 = Sophie Germain prime

1560 = pronic number

1561 = a centered octahedral number, number of series-reduced trees with 19 nodes

1562 = maximal number of regions the plane is divided into by drawing 40 circles

1563 = ${\displaystyle \sum _{k=1}^{50}{\frac {50}{\gcd(50,k)}}}$

1564 = sum of totient function for first 71 integers

1565 = ${\displaystyle {\sqrt {1036^{2}+1173^{2}}}}$ and ${\displaystyle 1036+1173=47^{2}}$

1566 = number k such that k + 1 is prime

1567 = number of partitions of 24 with at least one distinct part

1568 = Achilles number

1569 = 2 × 28 + 1 = number of different 2 × 2 determinants with integer entries from 0 to 28

1570 = 2 × 28 + 2 = number of points on surface of tetrahedron with edgelength 28

1571 = Honaker prime

1572 = member of the Mian–Chowla sequence

1573 = discriminant of a totally real cubic field

1574 + 1 is prime

1575 = odd abundant number, sum of the nontriangular numbers between successive triangular numbers, number of partitions of 24

1576 == 1 (mod 15^2)

1577 = sum of the quadratic residues of 83

1578 = sum of first 45 composite numbers

1579 = number of partitions of 54 such that the smallest part is greater than or equal to number of parts

1580 = number of achiral integer partitions of 51

1581 = number of edges in the hexagonal triangle T(31)

1582 = a number such that the integer triangle ※ has an integer area

1583 = Sophie Germain prime

1584 = triangular matchstick number

1585 = Riordan number, centered triangular number

1586 = area of the 23rd conjoined trapezoid

1587 = 3 × 23 = number of edges of a complete tripartite graph of order 69, K_23,23,23

1588 = sum of totient function for first 72 integers

1589 = composite de Polignac number

1590 = rounded volume of a regular icosahedron with edge length 9

1591 = rounded volume of a regular octahedron with edge length 15

1592 = sum of all divisors of the first 36 odd numbers

1593 = sum of the first 30 primes

1594 = minimal cost of maximum height Huffman tree of size 17

1595 = number of non-isomorphic set-systems of weight 10

1596 = triangular number

1597 = Fibonacci prime, Markov prime, super-prime, emirp

1598 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,25}

1599 = number of edges in the join of two cycle graphs, both of order 39

1600 to 1699※

1600 = 40, structured great rhombicosidodecahedral number, repdigit in base 7 (4444₇), 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, the novel 1601 (Mark Twain)

1602 = number of points on surface of octahedron with edgelength 20

1603 = number of partitions of 27 with nonnegative rank

1604 = number of compositions of 22 into prime parts

1605 = number of polyominoes consisting of 7 regular octagons

1606 = enneagonal pyramidal number

1607 = member of prime triple with 1609 and 1613

1608 = ${\displaystyle \sum _{k=1}^{44}\sigma (k)}$

1609 = cropped hexagonal number

1610 = number of strict partions of 43

1611 = number of rational numbers which can be constructed from the set of integers between 1 and 51

1612 = maximum dimension of Euclidean spaces which suffice for every smooth compact Riemannian 31-manifold to be realizable as a sub-manifold

1613, 1607 and 1619 are all primes

1614 = number of ways of refining the partition 8^1 to get 1^8

1615 = composite number such that the square mean of its prime factors is a nonprime integer

1616 = ${\displaystyle {\frac {16(16^{2}+3\times 16-1)}{3}}}$ = number of monotonic triples (x,y,z) in {1,2,...,16}

1617 = pentagonal number

1618 = centered heptagonal number

1619 = palindromic prime in binary, safe prime

1620 = 809 + 811: sum of twin prime pair

1621 = super-prime, pinwheel number

1622 = semiprime of the form prime + 1

1623 is not the sum of two triangular numbers and a fourth power

1624 = number of squares in the Aztec diamond of order 28

1625 = centered square number

1626 = centered pentagonal number

1627 = prime and 2 × 1627 - 1 = 3253 is also prime

1628 = centered pentagonal number

1629 = rounded volume of a regular tetrahedron with edge length 24

1630 = number k such that k^64 + 1 is prime

1631 = ${\displaystyle \sum _{k=0}^{5}(k+1)!{\binom {5}{k}}}$

1632 = number of acute triangles made from the vertices of a regular 18-polygon

1633 = star number

1634 = Narcissistic number in base 10

1635 = number of partitions of 56 whose reciprocal sum is an integer

1636 = number of nonnegative solutions to x + y ≤ 45

1637 = prime island: least prime whose adjacent primes are exactly 30 apart

1638 = harmonic divisor number, 5 × 2 - 1 is prime

1639 = nonagonal number

1640 = pronic number

1641 = 41 - 41 + 1 = H₄₁ (the 41st Hogben number)

1642 = maximal number of regions the plane is divided into by drawing 41 circles

1643 = sum of first 46 composite numbers

1644 = 821 + 823: sum of twin prime pair

1645 = number of 16-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection

1646 = number of graphs with 8 nodes and 14 edges

1647 and 1648 are both divisible by cubes

1648 = number of partitions of 34 into distinct cubes

1649 = highly cototient number, Leyland number

1650 = number of cards to build an 33-tier house of cards

1651 = heptagonal number

1652 = number of partitions of 29 into a prime number of parts

1653 = triangular number, hexagonal number, number of lattice points inside a circle of radius 23

1654 = number of partitions of 42 into divisors of 42

1655 = rounded volume of a regular dodecahedron with edge length 6

1656 = 827 + 829: sum of twin prime pair

1657 = cuban prime, prime of the form 2p-1

1658 = smallest composite that when added to sum of prime factors reaches a prime after 25 iterations

1659 = number of rational numbers which can be constructed from the set of integers between 1 and 52

1660 = sum of totient function for first 73 integers

1661 = 11 × 151, palindrome that is a product of two palindromic primes

1662 = number of partitions of 49 into pairwise relatively prime parts

1663 = a prime number and 5 - 4 is a 1163-digit prime number

1664 = k such that k, k+1 and k+2 are sums of 2 squares

1665 = centered tetrahedral number

1666 = largest efficient pandigital number in Roman numerals (each symbol occurs exactly once)

1667 = 228 + 1439 and the 228th prime is 1439

1668 = number of partitions of 33 into parts all relatively prime to 33

1669 = super-prime, smallest prime with a gap of exactly 24 to the next prime

1670 = number of compositions of 12 such that at least two adjacent parts are equal

1671 divides the sum of the first 1671 composite numbers

1672 = 41 - 3, the only way to express 1672 as a difference of prime squares

1673 = RMS number

1674 = k such that geometric mean of phi(k) and sigma(k) is an integer

1675 = Kin number

1676 = number of partitions of 34 into parts each of which is used a different number of times

1677 = 41 - 2, the only way to express 1677 as a difference of prime squares

1678 = n such that n + 1 is prime

1679 = highly cototient number, semiprime (23 × 73, see also Arecibo message), number of parts in all partitions of 32 into distinct parts

1680 = highly composite number, number of edges in the join of two cycle graphs, both of order 40

1681 = 41, smallest number yielded by the formula n + n + 41 that is not a prime; centered octagonal number

1682 = and 1683 is a member of a Ruth–Aaron pair (first definition)

1683 = triangular matchstick number

1684 = centered triangular number

1685 = 5-Knödel number

1686 = ${\displaystyle \sum _{k=1}^{45}\sigma (k)}$

1687 = 7-Knödel number

1688 = number of finite connected sets of positive integers greater than one with least common multiple 72

1689 = ${\displaystyle 9!!\sum _{k=0}^{4}{\frac {1}{2k+1}}}$

1690 = number of compositions of 14 into powers of 2

1691 = the same upside down, which makes it a strobogrammatic number

1692 = coreful perfect number

1693 = smallest prime > 41.

1694 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,26}

1695 = magic constant of n × n normal magic square and n-queens problem for n = 15. Number of partitions of 58 into prime parts

1696 = sum of totient function for first 74 integers

1697 = Friedlander-Iwaniec prime

1698 = number of rooted trees with 47 vertices in which vertices at the same level have the same degree

1699 = number of rooted trees with 48 vertices in which vertices at the same level have the same degree

1700 to 1799※

1700 = σ₂(39): sum of squares of divisors of 39

1701 = ${\displaystyle \left\{{8 \atop 4}\right\}}$, decagonal number, hull number of the U.S.S. Enterprise on 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

1704 = sum of the squares of the parts in the partitions of 18 into two distinct parts

1705 = tribonacci number

1706 = 1 + 4 + 16 + 64 + 256 + 1024 + 256 + 64 + 16 + 4 + 1 sum of fifth row of triangle of powers of 4

1707 = number of partitions of 30 in which the number of parts divides 30

1708 = 2 × 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

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 × 75616446785773

1710 = maximal number of pieces that can be obtained by cutting an annulus with 57 cuts

1711 = triangular number, centered decagonal number

1712 = number of irredundant sets in the 29-cocktail party graph

1713 = number of aperiodic rooted trees with 12 nodes

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

1715 = k such that geometric mean of phi(k) and sigma(k) is an integer

1716 = 857 + 859: sum of twin prime pair

1717 = pentagonal number

1718 = ${\displaystyle \sum _{d|12}{\binom {12}{d}}}$

1719 = composite de Polignac number

1720 = sum of the first 31 primes

1721 = twin prime; number of squares between 42 and 42.

1722 = Giuga number, pronic number

1723 = super-prime

1724 = maximal number of regions the plane is divided into by drawing 42 circles

1725 = 47 - 22 = (prime(15)) - (nonprime(15))

1726 = number of partitions of 44 into distinct and relatively prime parts

1727 = area of the 24th conjoined trapezoid

1728 = the quantity expressed as 1000 in 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 closed on Broadway in New York City after 1729 performances. Palindromic in bases 12, 32, 36.

1730 = 3 × 24 + 2 = number of points on surface of square pyramid of side-length 24

1731 = k such that geometric mean of phi(k) and sigma(k) is an integer

1732 = ${\displaystyle \sum _{k=0}^{5}{\binom {5}{k}}^{k}}$

1733 = Sophie Germain prime, palindromic in bases 3, 18, 19.

1734 = surface area of a cube of edge length 17

1735 = number of partitions of 55 such that the smallest part is greater than or equal to number of parts

1736 = sum of totient function for first 75 integers, number of surface points on a cube with edge-length 18

1737 = pinwheel number

1738 = number of achiral integer partitions of 52

1739 = number of 1s in all partitions of 30 into odd parts

1740 = number of squares in the Aztec diamond of order 29

1741 = super-prime, centered square number

1742 = number of regions the plane is divided into by 30 ellipses

1743 = wiener index of the windmill graph D(3,21)

1744 = k such that k, k+1 and k+2 are sums of 2 squares

1745 = 5-Knödel number

1746 = number of unit-distance graphs on 8 nodes

1747 = balanced prime

1748 = number of partitions of 55 into distinct parts in which the number of parts divides 55

1749 = number of integer partitions of 33 with no part dividing all the others

1750 = hypotenuse in three different Pythagorean triangles

1751 = cropped hexagone

1752 = 79 - 67, the only way to express 1752 as a difference of prime squares

1753 = balanced prime

1754 = k such that 5*2 - 1 is prime

1755 = number of integer partitions of 50 whose augmented differences are distinct

1756 = centered pentagonal number

1757 = least number of triangles of the Spiral of Theodorus to complete 13 revolutions

1758 = ${\displaystyle \sum _{k=1}^{46}\sigma (k)}$

1759 = de Polignac prime

1760 = the number of yards in a mile

1761 = k such that k, k+1 and k+2 are products of two primes

1762 = number of binary sequences of length 12 and curling number 2

1763 = number of edges in the join of two cycle graphs, both of order 41

1764 = 42

1765 = number of stacks, or planar partitions of 15

1766 = number of points on surface of octahedron with edgelength 21

1767 = σ(28) = σ(35)

1768 = number of nonequivalent dissections of an hendecagon into 8 polygons by nonintersecting diagonals up to rotation

1769 = maximal number of pieces that can be obtained by cutting an annulus with 58 cuts

1770 = triangular number, hexagonal number, Seventeen Seventy, town in Australia

1771 = tetrahedral number

1772 = centered heptagonal number, sum of totient function for first 76 integers

1773 = number of words of length 5 over the alphabet {1,2,3,4,5} such that no two even numbers appear consecutively

1774 = number of rooted identity trees with 15 nodes and 5 leaves

1775 = ${\displaystyle \sum _{1\leq i\leq 10}prime(i)\cdot (2\cdot i-1)}$: sum of piles of first 10 primes

1776 = 24th square star number. The number of pieces that could be seen in a 7 × 7 × 7× 7 Rubik's Tesseract.

1777 = smallest prime > 42.

1778 = least k >= 1 such that the remainder when 6 is divided by k is 22

1779 = number of achiral integer partitions of 53

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

1781 = the first 1781 digits of e form a prime

1782 = heptagonal number

1783 = de Polignac prime

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

1785 = square pyramidal number, triangular matchstick number

1786 = centered triangular number

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

1789 = number of wiggly sums adding to 17 (terms alternately increase and decrease or vice versa)

1790 = number of partitions of 50 into pairwise relatively prime parts

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

1794 = nonagonal number, number of partitions of 33 that do not contain 1 as a part

1795 = number of heptagons with perimeter 38

1796 = k such that geometric mean of phi(k) and sigma(k) is an integer

1797 = number k such that phi(prime(k)) is a square

1798 = 2 × 29 × 31 = 10₂ × 11101₂ × 11111₂, which yield zero when the prime factors are xored together

1799 = 2 × 30 − 1 = a twin square

1800 to 1899※

1800 = pentagonal pyramidal number, Achilles number, also, in da Ponte's Don Giovanni, the number of women Don Giovanni had slept with so far when confronted by Donna Elvira, according to Leporello's tally

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)

1802 = 2 × 30 + 2 = number of points on surface of tetrahedron with edgelength 30, number of partitions of 30 such that the number of odd parts is a part

1803 = number of decahexes that tile the plane isohedrally. But not by translation or by 180-degree rotation (Conway criterion)

1804 = number k such that k^64 + 1 is prime

1805 = number of squares between 43 and 43.

1806 = pronic number, product of first four terms of Sylvester's sequence, primary pseudoperfect number, only number for which n equals the denominator of the nth Bernoulli number, Schröder number

1807 = fifth term of Sylvester's sequence

1808 = maximal number of regions the plane is divided into by drawing 43 circles

1809 = sum of first 17 super-primes

1810 = ${\displaystyle \sum _{k=0}^{4}{\binom {4}{k}}^{4}}$

1811 = Sophie Germain prime

1812 = n such that n + 1 is prime

1813 = number of polyominoes with 26 cells, symmetric about two orthogonal axes

1814 = 1 + 6 + 36 + 216 + 1296 + 216 + 36 + 6 + 1 = sum of 4th row of triangle of powers of six

1815 = polygonal chain number ${\displaystyle \#(P_{2,1}^{3})}$

1816 = number of strict partions of 44

1817 = total number of prime parts in all partitions of 20

1818 = n such that n + 1 is prime

1819 = sum of the first 32 primes, minus 32

1820 = pentagonal number, pentatope number, number of compositions of 13 whose run-lengths are either weakly increasing or weakly decreasing

1821 = member of the Mian–Chowla sequence

1822 = number of integer partitions of 43 whose distinct parts are connected

1823 = super-prime, safe prime

1824 = 43 - 5, the only way to express 1824 as a difference of prime squares

1825 = octagonal number

1826 = decagonal pyramidal number

1827 = vampire number

1828 = meandric number, open meandric number, appears twice in the first 10 decimal digits of e

1829 = composite de Polignac number

1830 = triangular number

1831 = smallest prime with a gap of exactly 16 to next prime (1847)

1832 = sum of totient function for first 77 integers

1833 = number of atoms in a decahedron with 13 shells

1834 = octahedral number, sum of the cubes of the first five primes

1835 = absolute value of numerator of ${\displaystyle D_{6}^{(5)}}$

1836 = factor by which a proton is more massive than an electron

1837 = star number

1838 = number of unimodular 2 × 2 matrices having all terms in {0,1,...,27}

1839 = ${\displaystyle \lfloor {\sqrt※{13!}}\rfloor }$

1840 = 43 - 3, the only way to express 1840 as a difference of prime squares

1841 = solution to the postage stamp problem with 3 denominations and 29 stamps, Mertens function zero

1842 = number of unlabeled rooted trees with 11 nodes

1843 = k such that phi(k) is a perfect cube, Mertens function zero

1844 = 3 - 7, Mertens function zero

1845 = number of partitions of 25 containing at least one prime, Mertens function zero

1846 = sum of first 49 composite numbers

1847 = super-prime

1848 = number of edges in the join of two cycle graphs, both of order 42

1849 = 43, palindromic in base 6 (= 12321₆), centered octagonal number

1850 = Number of partitions of 59 into prime parts

1851 = sum of the first 32 primes

1852 = number of quantales on 5 elements, up to isomorphism

1853 = sum of primitive roots of 27-th prime, Mertens function zero

1854 = number of permutations of 7 elements with no fixed points, Mertens function zero

1855 = rencontres number: number of permutations of ※ with exactly one fixed point

1856 = sum of totient function for first 78 integers

1857 = Mertens function zero, pinwheel number

1858 = number of 14-carbon alkanes C₁₄H₃₀ ignoring stereoisomers

1859 = composite de Polignac number

1860 = number of squares in the Aztec diamond of order 30

1861 = centered square number, Mertens function zero

1862 = Mertens function zero, forms a Ruth–Aaron pair with 1863 under second definition

1863 = Mertens function zero, forms a Ruth–Aaron pair with 1862 under second definition

1864 = Mertens function zero, ${\displaystyle {\frac {1864!-2}{2}}}$ is a prime

1865 = 12345₆: Largest senary metadrome (number with digits in strict ascending order in base 6)

1866 = Mertens function zero, number of plane partitions of 16 with at most two rows

1867 = prime de Polignac number

1868 = smallest number of complexity 21: smallest number requiring 21 1's to build using +, * and ^

1869 = Hultman number: S_H(7, 4)

1870 = decagonal number

1871 = the first prime of the 2 consecutive twin prime pairs: (1871, 1873) and (1877, 1879)

1872 = first Zagreb index of the complete graph K₁₃

1873 = number of Narayana's cows and calves after 21 years

1874 = area of the 25th conjoined trapezoid

1875 = 50 - 25

1876 = number k such that k^64 + 1 is prime

1877 = number of partitions of 39 where 39 divides the product of the parts

1878 = n such that n + 1 is prime

1879 = a prime with square index

1880 = the 10th element of the self convolution of Lucas numbers

1881 = tricapped prism number

1882 = number of linearly separable Boolean functions in 4 variables

1883 = number of conjugacy classes in the alternating group A₂₈

1884 = k such that 5*2 - 1 is prime

1885 = Zeisel number

1886 = number of partitions of 6 into fourth powers

1887 = number of edges in the hexagonal triangle T(34)

1888 = primitive abundant number (abundant number all of whose proper divisors are deficient numbers)

1889 = Sophie Germain prime, highly cototient number

1890 = triangular matchstick number

1891 = triangular number, sum of 5 consecutive primes (367 + 373 + 379 + 383 + 389) hexagonal number, centered pentagonal number, centered triangular number

1892 = pronic number

1893 = 44 - 44 + 1 = H₄₄ (the 44th Hogben number)

1894 = maximal number of regions the plane is divided into by drawing 44 circles

1895 = Stern-Jacobsthal number

1896 = member of the Mian-Chowla sequence

1897 = member of Padovan sequence, number of triangle-free graphs on 9 vertices

1898 = smallest multiple of n whose digits sum to 26

1899 = cropped hexagone

1900 to 1999※

1900 = number of primes <= 2. Also 1900 (film) or 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

1903 = generalized catalan number

1904 = number of flat partitions of 43

1905 = Fermat pseudoprime

1906 = number n such that 3 - 8 is prime

1907 = safe prime, balanced prime

1908 = coreful perfect number

1909 = hyperperfect number

1910 = number of compositions of 13 having exactly one fixed point

1911 = heptagonal pyramidal number

1912 = size of 6th maximum raising after one blind in pot-limit poker

1913 = super-prime, Honaker prime

1914 = number of bipartite partitions of 12 white objects and 3 black ones

1915 = number of nonisomorphic semigroups of order 5

1916 = sum of first 50 composite numbers

1917 = number of partitions of 51 into pairwise relatively prime parts

1918 = heptagonal number

1919 = smallest number with reciprocal of period length 36 in base 10

1920 = sum of the nontriangular numbers between successive triangular numbers

1921 = 4-dimensional centered cube number

1922 = Area of a square with diagonal 62

1923 = 2 × 31 + 1 = number of different 2 X 2 determinants with integer entries from 0 to 31

1924 = 2 × 31 + 2 = number of points on surface of tetrahedron with edgelength 31

1925 = number of ways to write 24 as an orderless product of orderless sums

1926 = pentagonal number

1927 = 2 - 11

1928 = number of distinct values taken by 2^2^...^2 (with 13 2's and parentheses inserted in all possible ways)

1929 = Mertens function zero, number of integer partitions of 42 whose distinct parts are connected

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

1931 = Sophie Germain prime

1932 = number of partitions of 40 into prime power parts

1933 = centered heptagonal number, Honaker prime

1934 = sum of totient function for first 79 integers

1935 = number of edges in the join of two cycle graphs, both of order 43

1936 = 44, 18-gonal number, 324-gonal number.

1937 = number of chiral n-ominoes in 12-space, one cell labeled

1938 = Mertens function zero, number of points on surface of octahedron with edgelength 22

1939 = 7-Knödel number

1940 = the Mahonian number: T(8, 9)

1941 = maximal number of regions obtained by joining 16 points around a circle by straight lines

1942 = number k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes

1943 = largest number not the sum of distinct tetradecagonal numbers

1944 = 3-smooth number (2×3), Achilles number

1945 = number of partitions of 25 into relatively prime parts such that multiplicities of parts are also relatively prime

1946 = number of surface points on a cube with edge-length 19

1947 = k such that 5·2 + 1 is a prime factor of a Fermat number 2 + 1 for some m

1948 = number of strict solid partitions of 20

1949 = smallest prime > 44.

1950 = ${\displaystyle 1\cdot 2\cdot 3+4\cdot 5\cdot 6+7\cdot 8\cdot 9+10\cdot 11\cdot 12}$, largest number not the sum of distinct pentadecagonal numbers

1951 = cuban prime

1952 = number of covers of {1, 2, 3, 4}

1953 = triangular number

1954 = number of sum-free subsets of {1, ..., 16}

1955 = number of partitions of 25 with at least one distinct part

1956 = nonagonal number

1957 = ${\displaystyle \sum _{k=0}^{6}{\frac {6!}{k!}}}$ = total number of ordered k-tuples (k=0,1,2,3,4,5,6) of distinct elements from an 6-element set

1958 = number of partitions of 25

1959 = Heptanacci-Lucas number

1960 = number of parts in all partitions of 33 into distinct parts

1961 = number of lattice points inside a circle of radius 25

1962 = number of edges in the join of the complete graph K₃₆ and the cycle graph C₃₆

1963! - 1 is prime

1964 = number of linear forests of planted planar trees with 8 nodes

1965 = total number of parts in all partitions of 17

1966 = sum of totient function for first 80 integers

1967 = least edge-length of a square dissectable into at least 30 squares in the Mrs. Perkins's quilt problem

σ(1968) = σ(1967) + σ(1966)

1969 = Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize

1970 = number of compositions of two types of 9 having no even parts

1971 = ${\displaystyle 3^{7}-6^{3}}$

1972 = n such that ${\displaystyle {\frac {n^{37}-1}{n-1}}}$ is prime

1973 = Sophie Germain prime, Leonardo prime

1974 = number of binary vectors of length 17 containing no singletons

1975 = number of partitions of 28 with nonnegative rank

1976 = octagonal number

1977 = number of non-isomorphic multiset partitions of weight 9 with no singletons

1978 = n such that n | (3 + 5)

1979 = number of squares between 45 and 45.

1980 = pronic number

1981 = pinwheel number

1982 = maximal number of regions the plane is divided into by drawing 45 circles

1983 = skiponacci number

1984 = 11111000000 in binary, see also: 1984 (disambiguation)

1985 = centered square number

1986 = number of ways to write 25 as an orderless product of orderless sums

1987 = 300th prime number

1988 = sum of the first 33 primes

1989 = number of 9-step mappings with 4 inputs

1990 = Stella octangula number

1991 = 11 × 181, the 46th Gullwing number, palindromic composite number with only palindromic prime factors

1992 = number of nonisomorphic sets of nonempty subsets of a 4-set

1993 = a number with the property that 4 - 3 is prime, number of partitions of 30 into a prime number of parts

1994 = Glaisher's function W(37)

1995 = number of unlabeled graphs on 9 vertices with independence number 6

1996 = a number with the property that (1996! + 3)/3 is prime

1997 = ${\displaystyle \sum _{k=1}^{21}{k\cdot \phi (k)}}$

1998 = triangular matchstick number

1999 = centered triangular number number of regular forms in a myriagram.

Prime numbers※

There are 135 prime numbers between 1000 and 2000:

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

Notes※

References※