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 units 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. It is the first 4-digit integer.
Contents
Notation
The decimal representation for one thousand is
1000—a one followed by three zeros, in the general notation;
1 × 103—in engineering notation, which for this number coincides with:
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 or 210).
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 using "Y2K" to denote the Year 2000 computer problem.
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.
In mathematics
A chiliagon is a 1000-sided polygon.
Numbers in the range 1001–1999
1001 to 1099
1002 = 2 × 3 × 167. It is a sphenic number, an abundant number, and a zero of Mertens function. There are 1002 partitions of 22.
1003 = the product of some prime p and the pth prime, namely p = 17.
1004 = 22 × 251. It is a heptanacci number.
1005 = k(GL(5, 4)), the number of conjugacy classes in GL(5, 4)
1006 = 2 × 503. It is an unusual number, an equidigital number, and a square-free number. It is a record gap between twin primes. There are 1006 compositions (ordered partitions) of 22 into squares 1006 undirected Hamiltonian paths in 4 by 5 square grid graph.
1009 is the smallest four-digit prime, a Lucky prime, and Chen prime. It is palindromic in bases 11, 15, 19, 24 and 28: (83811, 47415, 2F219, 1I124, 18128).
1011 = 3 × 337. It is a Harshad number in bases 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75 (and 202 other bases). It is the largest natural number n such that 2n contains 101 and does not contain 11011. There are 1011 partitions of 1 into reciprocals of positive integers <= 16 Egyptian fraction.
1012 = 22 × 11 × 23. There are 1012 partitions of 1 into reciprocals of positive integers <= 17 Egyptian fraction.
1013 is a prime number, a Sophie Germain prime, and a centered square number,
1016 = 23 × 127. It is stella octangula number and a member of the Mian–Chowla sequence. There are 1016 surface points on a cube with edge-length 14.
1019 is a prime number, a Sophie Germain prime, a safe prime, and a Chen prime.
1100 to 1199
1102 = 2 × 19 × 29. It is the sum of the totient function for the first 60 integers.
1103 is a prime number, a Sophie Germain prime, and a balanced prime.
1104 = 24 × 3 × 23. It is a Keith number
1107 = 33 × 41. There are 1107 non-isomorphic strict T0 multiset partitions of weight 8.
1109 is a Friedlander-Iwaniec prime and a Chen prime.
1113 = 3 × 7 × 53. There are 1113 strict partions of 40.
1114 = 2 × 557. There are 1114 ways to write 22 as an orderless product of orderless sums.
1117 is a Chen prime. There are 1117 diagonally symmetric polyominoes with 16 cells.
1118 = 2 × 13 × 43. There are 1118 unimodular 2 × 2 matrices having all terms in {0,1,...,21}.
1119 = 3 × 373. There are 1119 bipartite graphs with 9 nodes.
1122 = 2 × 3 × 11 × 17. It is a pronic number.
1123 is a balanced prime.
1124 = 22 × 281. It is a Leyland number using 2 & 10: 1124 = 210 + 102. It is a spy number.
1126 = 2 × 563. There are 1126 2 × 2 non-singular integer matrices with entries from {0, 1, 2, 3, 4, 5}.
1127 = 72 × 23. It is the maximum number of pieces that can be obtained by cutting an annulus with 46 cuts.
1200 to 1299
1200 = 24 × 3 × 52. There are 1200 households in the Nielsen ratings sample.
1200 is known as the long thousand or ten "long hundreds" of 120 each. It is the traditional reckoning of large numbers in Germanic languages.
1201 is a super-prime, a centered square number, and a centered decagonal number.
1202 = 2 × 601. There are a maximum of 1202 regions when the plane is divided by 25 ellipses.
1203 = 3 × 401. It is the smallest number greater than 1000 in the coordinating sequence for the (2,6,∞) tiling of the hyperbolic plane.
1204 = 22 × 7 × 43. It is the magic constant for a 7 × 7 × 7 magic cube.
1205 = 5 × 241. There are 1205 partitions of 28 such that the number of odd parts is a part
1207 = 17 × 71. It is a composite de Polignac number.
1208 = 23 × 151. There are 1208 strict chains of divisors starting with the superprimorial A006939(3).
1210 = 2 × 5 × 112. It is an amicable number with 1184 and a Self-descriptive number.
1211 = 7 × 173. It is a composite de Polignac number
1212 = 22 × 3 × 101 =
∑
k
=
0
1300 to 1399
1300 = 22 × 52 × 13. It is a zero of Mertens function and the smallest even odd-factor hyperperfect number. It is the sum of the first 4 fifth powers:
1300 = 15 + 25 + 35 + 45.
1301 is a prime number and a centered square number. There are 1301 trees with 13 unlabeled nodes.
1306 = 2 × 653. It is a centered triangular number.
1307 is a safe prime.
1308 = 22 × 3 × 109. It is the sum of the totient function for the first 65 integers.
1312 = 25 × 41. It is a member of the Mian-Chowla sequence.
1319 is a safe prime.
1325 = 52 × 53. It is a Markov number and a centered tetrahedral number.
1326 = 2 × 3 × 13 × 17. It is the 51st triangular number and a hexagonal number.
1327 is the smallest prime number preceding a prime gap of 34.
1328 = 24 × 83. It is the sum of the totient function for the first 66 integers.
1330 = 2 × 5 × 7 × 19. It is a tetrahedral number. It forms a Ruth–Aaron pair with 1331 under second definition.
1331 = 113. It is a centered heptagonal number. It forms a Ruth–Aaron pair with 1330 under second definition.
1335 = 3 × 5 × 89. It is a pentagonal number.
1400 to 1499
1403 = 23 × 61. It is the smallest number x such that M(x) = 11, where M() is Mertens function
1404 = 22 × 32 × 13. It is a heptagonal number.
1405 = 5 × 281 = 262 + 272 = 72 + 82 + ... + 162. It is a centered square number
1406 = 2 × 19 × 37. It is a semi-meandric number.
1409 is a super-prime, a Sophie Germain prime, and a Proth prime.
1410 = 2 × 3 × 5 × 47. It is the denominator of the 46th Bernoulli number
1418 = 2 × 709. It is the smallest number x such that M(x) = 13, where M() is Mertens function
1425 = 3 × 52 × 19. It is a self-descriptive number in base 5.
1426 = 2 × 23 × 31. It is a pentagonal number and the sum of the totient function for the first 68 integers. There are 1426 strict partions of 42.
1427 is a twin prime with 1429.
1428 = 22 × 3 × 7 × 17. There are 1428 complete ternary trees with 6 internal nodes or, equivalently, 18 edges.
1429 is a twin prime with 1427.
1430 = 2 × 5 × 11 × 13. It is a Catalan number.
1431 = 33 × 53. It is the 53rd triangular number and a hexagonal number.
1432 = 23 × 179. It is a member of the Padovan sequence.
1500 to 1599
1500 = 22 × 3 × 53. It is the hypotenuse of three different Pythagorean triangles.
1501 = 19 × 79. It is a centered pentagonal number.
1503 = 32 × 167. Completing 12 revolutions of the Spiral of Theodorus requires 1503 triangles.
1510 = 2 × 5 × 151. 1510 is an untouchable number.
1511 is a Sophie Germain prime and a balanced prime.
1513 = 17 × 89. It is a centered square number.
1520 = 24 × 5 × 19. It is a pentagonal number. It forms a Ruth–Aaron pair with 1521 under the second definition.
1521 = 32 × 132 = 392. It is a centered octagonal number. It forms a Ruth–Aaron pair with 1520 under the second definition.
1523 is a super-prime, a safe prime, and a member of the Mian–Chowla sequence.
1525 = 52 × 61. It is a heptagonal number.
1526 = 2 × 7 × 109. There are 1526 conjugacy classes in the alternating group A27.
1529 = 11 × 139. It is a composite de Polignac number.
1530 = 2 × 32 × 5 × 17. It is a vampire number.
1531 is a prime number and a centered decagonal number.
1532 = 22 × 383. There are 1532 series-parallel networks with 9 unlabeled edges,
1600 to 1699
1601 is a Sophie Germain prime and a Proth prime.
1607, 1609, and 1613 form a prime triple.
1617 = 3 × 72 × 11. It is a pentagonal number.
1618 = 2 × 809. It is a centered heptagonal number.
1619 is a safe prime.
1621 is a super-prime.
1624 = 23 × 7 × 29. There are 1624 squares in the Aztec diamond of order 28.
1625 = 53 × 13. It is a centered square number.
1626 = 2 × 3 × 271. It is a centered pentagonal number.
1633
1633 = 23 × 71. It is a star number.
1634 = 2 × 19 × 43. It is the smallest four-digit Narcissistic number in base 10.
1637 is a prime island: it is the smallest prime whose adjacent primes are exactly 30 apart.
1638 = 2 × 32 × 7 × 13. It is a harmonic divisor number.
1639 = 11 × 149. It is a nonagonal number.
1646 = 2 × 823. There are 1646 graphs with 8 nodes and 14 edges.
1649 = 17 × 97. It is a highly cototient number and a Leyland number using 4 and 5: 1649 = 45 + 54.
1651 = 13 × 127. It is a heptagonal number.
1700 to 1799
1705 = 5 × 11 × 13. It is a tribonacci number.
1710 = 2 × 32 × 5 × 19. A maximum of 1710 pieces can be obtained by cutting an annulus 57 times.
1711 = 29 × 59. It is the 58th triangular number and a centered decagonal number.
1717 = 17 × 101. It is a pentagonal number.
1719 = 32 × 131. it is a composite de Polignac number.
1720 = 23 × 5 × 43. It is the sum of the first 31 primes.
1721 is a twin prime with 1723.
1722 = 2 × 3 × 7 × 41. It is a Giuga number and a pronic number.
1723 is a twin prime with 1721. It is also a super-prime.
1733 is a Sophie Germain prime. It is palindromic in bases 3, 18, and 19.
1736 = 23 × 7 × 31. It is the sum of the totient function for the first 75 integers.
1740 = 22 × 3 × 5 × 29. There are 1740 squares in the Aztec diamond of order 29.
1741 is a super-prime and a centered square number.
1747 is a balanced prime.
1750 = 2 × 53 × 7. It is the hypotenuse of three different Pythagorean triangles with integer side lengths.
1753 is a balanced prime.
1800 to 1899
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)
1803 = number of decahexes that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion)
1806 = pronic number, 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
1811 = Sophie Germain prime
1820 = pentagonal number, pentatope number,
1821 = member of the Mian–Chowla sequence
1823 = super-prime, safe prime
1825 = octagonal number
1827 = vampire number
1828 = meandric number, open meandric number
1829 = composite de Polignac number
1830 = 60th 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
1900 to 1999
1901 = Sophie Germain prime, centered decagonal number
1902 = number of symmetric plane partitions of 27
1903 = generalized Catalan number
1905 = Fermat pseudoprime
1907 = safe prime, balanced prime
1909 = hyperperfect number
1913 = super-prime
1918 = heptagonal number
1926 = pentagonal number
1931 = Sophie Germain prime
1933 = centered heptagonal number,
1934 = sum of totient function for first 79 integers
1941 = maximal number of regions obtained by joining 16 points around a circle by straight lines
1948 = number of strict solid partitions of 20
1951 = cuban prime
1952 = number of covers of {1, 2, 3, 4}
1953 = hexagonal prism number, 62nd triangular number
1956 = nonagonal number
1957 =
∑
k
=
0
Prime numbers
There are 135 prime numbers between 1000 and 2000:
Article from Wikipedia (CC BY-SA 4.0), where it is maintained by volunteer editors.
1021 is a prime number, a Lucky prime, and a twin prime with 1019.
1025 = 52 × 41. It is a Jacobsthal-Lucas number and the hypotenuse of a primitive Pythagorean triangle. It is a Proth number because 1025 = 210 + 1. It is a member of the Moser–de Bruijn sequence because its base-4 representation (1000014) contains only digits 0 and 1, or equivalently, it's a sum of distinct powers of 4 (45 + 40).
1028 = 22 × 257. It is sum of totient function for first 58 integers.
There are 1029 primes <= 213.
1031 is a prime number, a Sophie Germain prime, a super-prime, and a Chen prime. It is the exponent and number of ones for the fifth base-10 repunit prime.
1033 is a prime number and an emirp. It forms a twin prime pair with 1031.
1035 = 32 × 5 × 23. It is a hexagonal number and the 45th triangular number.
1039 is a prime of the form 8n+7, a Chen prime, and a Lucky prime. There are 1039 partitions of 30 that do not contain 1 as a part.
1040 = 24 × 5 × 13. There are 1040 pieces that could be seen in a 6 × 6 × 6× 6 Rubik's Tesseract.
1046 = 2 × 523. It is a coefficient of f(q), the 3rd order mock theta function.
1047 = 3 × 349. There are 1047 ways to split a strict composition of 18 into contiguous subsequences that have the same sum.
1049 is a prime number, a Sophie Germain prime, a highly cototient number, and a Chen prime.
1051 is a prime number, a centered pentagonal number, and a centered decagonal number.
1056 = 25 × 3 × 11. It is a pronic number.
1060 = 22 × 5 × 53. It is the sum of the first twenty-five primes from 2 through 97 (the number of primes less than 100) and the sixth sum of 10 consecutive primes, starting with 23 through 131.
1061 is a prime number, an emirp, and a twin prime with 1063. There are 1061 prime numbers between 1000 and 10000 (or, number of four-digit primes in decimal representation).
1063 is a prime number, a super-prime, a twin prime with 1061, a near-wall-sun-sun prime. and the sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167)
1069 is a prime number and an emirp.
1076 = 22 × 269. There are 1076 strict trees weight 11.
1078 = 2 × 72 × 11. It is an Euler transform of negative integers.
1080 = 23 × 33 × 5. It is a pentagonal number and a largely composite number.
1081 = 23 × 47. It is the 46th triangular number and a member of Padovan sequence.
1086 = 2 × 3 × 181. It is a Smith number and the sum of totient function for the first 59 integers.
1087 is a prime number, a super-prime, a cousin prime, and a lucky prime.
1091 is a prime number, a cousin prime, and a twin prime with 1093.
1093 is a twin prime with 1091. Together with 1091 and 1097, it forms a prime triplet. It is a happy prime and a star prime. It is also the smallest Wieferich prime. 1093 is a repunit prime in base 3 because:
1096 = 23 × 137. There are 1096 strict solid partitions of 18.
1097 is a prime number, an emirp, and a Chen prime.
1128 = 23 × 3 × 47. It is the 47th triangular number and the 24th hexagonal number. 1128 is the dimensional representation of the largest vertex operator algebra with central charge of 24, D24.
1151 is the first prime number following a prime gap of 22. It is also a Chen prime.
1152 = 27 × 32. It is a highly totient number, a 3-smooth number, and an Achilles number.
1153 is a super-prime and a Proth prime.
1159 = 19 × 61. It is a centered octahedral number and a member of the Mian–Chowla sequence.
1160 = 23 × 5 × 29. It is an octagonal number.
1161 = 33 × 43. It is the sum of the first twenty-six primes.
1162 = 2 × 7 × 83. It is the sum of the totient function for the first 61 integers and a pentagonal number.
1163 is a Chen prime.
1164 = 22 × 3 × 97. There are 1164 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
1169 = 7 × 167. It is a highly cototient number
1171 is a super-prime.
1173 = 3 × 17 × 23. There are 1173 simple triangulations on a plane with 9 nodes.
1174 = 2 × 587. There are 1174 widely totally strongly normal compositions of 16. (sequence A332337 in the OEIS).
1175 = 52 × 47. It is the maximum number of pieces that can be obtained by cutting an annulus with 47 cuts.
1176 = 23 × 3 × 72. It is the 48th triangular number.
1178 = 2 × 19 × 31. There are 1178 surface points on a cube with edge-length 15.
1179 = 32 × 131. There are 1179 different permanents of binary 7 by 7 matrices.
1182 = 2 × 3 × 197. There are 1182 necklaces possible with 14 beads of 2 colors (that cannot be turned over).
1184 = 25 × 37. It is an amicable number with 1210.
1186 = 2 × 593. There are 1186 diagonally symmetric polyominoes with 15 cells.
1187 is a safe prime, a Stern prime, a balanced prime, and a Chen prime.
1190 = 2 × 5 × 7 × 17. It is a pronic number. Building a 28-tier house of cards requires 1190 cards.
1192 = 23 × 149. It is the sum of the totient function for the first 62 integers.
1193 is a Chen prime.
41193 - 31193 is prime.
1198 = 2 × 599. It is a centered heptagonal number.
17
p
(
k
)
{\displaystyle \sum _{k=0}^{17}p(k)}
, where
p
(
k
)
{\displaystyle p(k)}
is the number of partions of
k
{\displaystyle k}
.
1213 is a prime number and an emirp.
1214 = 2 × 607. It is a spy number and the sum of the first 39 composite numbers.
1215 = 35 × 5. There are 1215 edges in the hexagonal triangle T(27)
1216 = 26 × 19. It is a nonagonal number
1217 is a super-prime and a Proth prime.
1219 = 23 × 53. It is a centered triangular number and a zero of Mertens function.
1220 = 22 × 5 × 61. It is a zero of Mertens function. There are 1220 binary vectors of length 16 containing no singletons.
1222 = 2 × 13 × 47. It is a hexagonal pyramidal number.
1223 is the 200th prime number. It is also a Sophie Germain prime and a balanced prime.
1224 = 23 × 32 × 17. There are 1224 edges in the join of two cycle graphs, both of order 34.
1225 = 52 × 72 = 352. It is the smallest number greater than 1 to be a triangular number, a square number and a hexagonal number. It is the second square triangular number greater than 1. It is the 49th triangular number, the 35th square number, the 25th hexagonal number, a centered octagonal number, a 29-gonal number, a 60-gonal number, and a 124-gonal number. It is the sum of 5 consecutive odd cubes:
1225 = 13 + 33 + 53 + 73 + 93.
1226 = 2 × 613. There are 1226 rooted identity trees with 15 nodes.
1228 = 22 × 307. It is the sum of the totient function for the first 63 integers.
1229 is a Sophie Germain prime and an emirp. There are 1229 primes less than 10,000.
1232 = 24 × 7 × 11. There are 1232 labeled ordered set of partitions of a 7-set into odd parts.
1240 = 23 × 5 × 31. It is a square pyramidal number.
1241 = 17 × 73. It is a centered cube number and a spy number.
1243 = 11 × 113. It is a composite de Polignac number.
1244 = 22 × 311. There are 1244 complete partitions of 25.
1245 = 3 × 5 × 83. There are 1245 labeled spanning intersecting set-systems on 5 vertices.
1247 = 29 × 43. It is a pentagonal number.
1249 is a prime number, an emirp, and a trimorphic number.
1257 = 3 × 419. There are 1257 lattice points inside a circle of radius 20.
1259 is a prime number and a highly cototient number.
1260 = 22 × 32 × 5 × 7. It is a pronic number, the smallest vampire number, the 16th highly composite number, and the sum of the totient function for the first 64 integers. There are 1260 strict partions of 41.
1261 = 13 × 97. It is a star number and a zero of Mertens function.
1264 = 24 × 79. It is the sum of the first 27 primes.
1265 = 5 × 11 × 23. There are 1265 rooted trees with 43 vertices in which vertices at the same level have the same degree.
1266 = 2 × 3 × 211. It is a centered pentagonal number and a zero of Mertens function.
1269 = 33 × 47. Completing 11 revolutions in the Spiral of Theodorus requires 1269 triangles.
1275 = 3 × 52 × 17. It is the 50th triangular number.
1276 = 22 × 11 × 29. There are 1276 irredundant sets in the 25-cocktail party graph.
1277 is a prime number. It is the start of a prime constellation of length 9 (a "prime nonuple").
1278 = 2 × 32 × 71. There are 1278 Narayana's cows and calves after 20 years.
1279 is a prime number and a Mersenne prime exponent.
1280 = 28 × 5. There are 1280 parts in all compositions of 9.
1281 = 3 × 7 × 61. It is an octagonal number.
1283 is a safe prime.
1284 = 22 × 3 × 107 = 641 + 643, the sum of a twin prime pair.
1285 = 5 × 257. There are 1285 free nonominoes.
1286 = 2 × 643. There are 1286 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.
1288 = 23 × 7 × 23. It is a heptagonal number.
1289 is Sophie Germain prime and a twin prime with 1291. 1289 is a deficient number because the sum of all its positive divisors (except itself) totals less than 1289. 1289 is an evil number because it has an even number of 1's contained in its binary expansion.
1291 is a twin prime with 1289.
1296 = 24 × 34 = 64 = 362. It is the sum of the cubes of the first eight positive integers:
There are 1296 rectangles on a normal 8 × 8 chessboard. There are 1296 combinations of 2 alphanumeric characters.
1297 is a super-prime, a pinwheel number, and a zero of Mertens function.
1342 = 2 × 11 × 61 =
∑
k
=
1
40
σ
(
k
)
{\displaystyle \sum _{k=1}^{40}\sigma (k)}
.
1346 = 2 × 673. There are 1346 locally disjointed rooted trees with 10 nodes.
1350 = 2 × 33 × 52. It is a nonagonal number.
1361 is first prime number following a prime gap of 34 and the 3rd Mills' prime. It is a centered decagonal number
1364 = 22 × 11 × 31. It is a Lucas number.
1365 = 3 × 5 × 7 × 13. It is a pentatope number.
1367 is a safe prime and a balanced prime. It is the 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),
1371 = 3 × 457. It is the sum of the first 28 primes.
1377 = 34 × 17. It is the maximal number of pieces that can be obtained by cutting an annulus with 51 cuts
1378 = 2 × 13 × 53. It is the 52nd triangular number
1379 = 7 × 197. It is the magic constant of n × n normal magic square and n-queens problem for n = 14.
1380 = 22 × 3 × 5 × 23. There are 1380 8-step mappings with 4 inputs.
1381 is a prime number and a centered pentagonal number.
1384 = 23 × 173 =
∑
k
=
1
41
σ
(
k
)
{\displaystyle \sum _{k=1}^{41}\sigma (k)}
1385 = 5 × 277. It is an up/down number.
1387 = 19 × 73. It is the 5th Fermat pseudoprime of base 2, the 22nd centered hexagonal number, the 19th decagonal number, and the second Super-Poulet number.
1388 = 22 × 347. Because 1388 = 4 × 192 - 3 × 19 + 1, is on the x-axis of Ulams spiral.
1394 = 2 × 17 × 41. It is the sum of the totient function for the first 67 integers.
1395 = 32 × 5 × 19. It is a vampire number and a member of the Mian–Chowla sequence
1396 = 22 × 349. It is a centered triangular number.
1399 is a prime number and an emirp.
1433 is a super-prime.
1435 = 5 × 7 × 41. It is a vampire number.
1436 = 22 × 359. It is the discriminant of a totally real cubic field.
1439 is a Sophie Germain prime and a safe prime.
1440 = 25 × 32 × 5. It is a highly totient number.
1441 = 11 × 131. It is a star number.
1447 is a super-prime number and a happy number.
1451 is a Sophie Germain prime.
1452 = 22 × 3 × 112. It is the first Zagreb index of the complete graph K12.
1453
1453 is a Sexy prime with 1459.
1458 = 2 × 36. It is the maximum determinant of an 11 by 11 matrix of zeroes and ones and a 3-smooth number.
1458 is one of three numbers which, when its base 10 digits are added together, produces a sum which, when multiplied by its reversed self, yields the original number:
1 + 4 + 5 + 8 = 18
18 × 81 = 1458
The only other non-trivial numbers with this property are 81 and 1729, as well as the trivial solutions 1 and 0. It was proven by Masahiko Fujiwara.
1459 is a Sexy prime with 1453 and a Pierpont prime. It is the sum of nine consecutive primes:
1462 = 2 × 17 × 43. Because 1462 = (35 - 1) × (35 + 8), it is the first Zagreb index of the wheel graph with 35 vertices
1467 = 32 × 163. There are 1467 partitions of 39 with zero crank.
1469 = 13 × 113. It is an octahedral number and a highly cototient number.
1470 = 2 × 3 × 5 × 72. It is the sum of the totient function for the first 69 integers.
1476 is the number of diamonds necessary to build a full, maximum-power (Level 4) pyramid for a Minecraft Beacon entirely out of diamond blocks.
1471 is a super-prime number and a centered heptagonal number.
1480 = 23 × 5 × 37. It is the sum of the first 29 primes.
1481 is a Sophie Germain prime.
1485 = 33 × 5 × 11. It is the 54th triangular number.
1486 = 2 × 743. There are 1486 strict solid partitions of 19.
1487 is a safe prime.
1489 is a prime number and a centered triangular number.
1490 = 2 × 5 × 149. It is a tetranacci number.
1491 = 3 × 7 × 71. It is a nonogonal number.
1492 = 22 × 373. It is the discriminant of a totally real cubic field.
1493 is a Stern prime.
1494 = 2 × 32 × 83. It is the sum of the totient function for the first 70 integers.
1496 = 23 × 11 × 17. It is a square pyramidal number.
1499 is a Sophie Germain prime and a super-prime.
1535 = 5 × 307. It is a Thabit number.
1537 = 29 × 53. It is a Keith number.
1539 = 34 × 19. A maximum of 1539 pieces can be obtained by cutting an annulus with 54 cuts.
1540 = 22 × 5 × 7 × 11. It is the 55th triangular number, a hexagonal number, a decagonal number, and a tetrahedral number.
1541 = 23 × 67. It is an octagonal number.
1549 is a de Polignac prime.
1557 = 32 × 173. There are 1557 graphs with 8 nodes and 13 edges.
1559 is a Sophie Germain prime.
1561 = 7 × 223. It is a centered octahedral number.
1564 = 22 × 17 × 23. It is the sum of the totient function for the first 71 integers.
1572 = 22 × 3 × 131. It is a member of the Mian–Chowla sequence.
1573 = 112 × 13. It is the discriminant of a totally real cubic field.
1583 is a Sophie Germain prime.
1585 = 5 × 307. It is a centered triangular number.
1588 = 22 × 397. It is the sum of the totient function for the first 72 integers.
1589 = 7 × 227. It is a composite de Polignac number.
1593 = 33 × 59. It is the sum of the first 30 primes.
1594 = 2 × 797. It is the minimal cost of a maximum height Huffman tree of size 17.
1596 = 22 × 3 × 7 × 19. It is the 56th triangular number.
1597 is a super-prime, a Fibonacci prime, a Markov prime, and an emirp.
1653 = 3 × 19 × 29. It is the 57th triangular number and a hexagonal number.
1657 is a cuban prime.
1660 = 22 × 5 × 83. It is the sum of the totient function for the first 73 integers.
1665 = 32 × 5 × 37. It is a centered tetrahedral number.
1669 is a super-prime. It is the smallest prime with a gap of exactly 24 to the next prime.
1679
1679 = 23 × 73. It is a highly cototient number.
1680 = 24 × 3 × 5 × 7. It is the 17th highly composite number.
1681 = 412 = 402 + 40 + 41. It is the smallest number yielded by the formula n2 + n + 41, where n is a natural number, that is not a prime. It is also a centered octagonal number.
1682 and 1683 form a Ruth–Aaron pair under the first definition.
1684 = 22 × 421. It is a centered triangular number.
1691 = 19 × 89. It is a strobogrammatic number.
1695 = 3 × 5 × 113. It is the magic constant of n × n normal magic square and the n-queens problem for n = 15.
1696 = 25 × 53. It is the sum of the totient function for the first 74 integers.
1756 = 22 × 439. It is a centered pentagonal number.
1757 = 7 × 251. Completing 13 revolutions around the Spiral of Theodorus requires 1757 triangles.
1759 is a de Polignac prime.
1765 = 5 × 353. There are 1765 planar partitions of 15.
1769 = 29 × 61. A maximum of 1769 pieces can be obtained by cutting an annulus with 58 times.
1770 = 2 × 3 × 59. It is the 59th triangular number and a hexagonal number.
1771 = 7 × 11 × 23. It is a tetrahedral number.
1772 = 22 × 443. It is a centered heptagonal number and the sum of the totient function for the first 76 integers.
1776 = 24 × 3 × 37. It is the 24th square star number. A total of 1776 pieces could be seen in a 7 × 7 × 7 × 7 Rubik's Tesseract.
1782 = 2 × 34 × 11. It is a heptagonal number.
1783 is a de Polignac prime.
1785 = 3 × 5 × 7 × 17. It is a square pyramidal number.
1786 = 2 × 19 × 47. It is a centered triangular number.
1787 is a super-prime. It is the sum of eleven consecutive primes: 1787 = 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191.
1792 = 28 × 7. It is a Granville number.
1794 = 2 × 3 × 13 × 23. It is a nonagonal number.
1835 = absolute value of numerator of
D
6
(
5
)
{\displaystyle D_{6}^{(5)}}
1837 = star number
1841 = solution to the postage stamp problem with 3 denominations and 29 stamps,
1842 = number of unlabeled rooted trees with 11 nodes
1847 = super-prime
1851 = sum of the first 32 primes
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 [7] with exactly one fixed point
1856 = sum of totient function for first 78 integers
1859 = composite de Polignac number
1860 = number of squares in the Aztec diamond of order 30
1861 = centered square number,
1862 = forms a Ruth–Aaron pair with 1863 under second definition
1863 = forms a Ruth–Aaron pair with 1862 under second definition
1867 = prime de Polignac number
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
1880 = the 10th element of the self convolution of Lucas numbers
1882 = number of linearly separable Boolean functions in 4 variables
1883 = number of conjugacy classes in the alternating group A28
1887 = number of edges in the hexagonal triangle T(34)
1889 = Sophie Germain prime, highly cototient number
1891 = 61st triangular number, sum of 5 consecutive primes (367 + 373 + 379 + 383 + 389) hexagonal number, centered pentagonal number, centered triangular number
1892 = pronic number
1896 = member of the Mian-Chowla sequence
1897 = member of Padovan sequence, number of triangle-free graphs on 9 vertices
6
6
!
k
!
{\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
1964 = number of linear forests of planted planar trees with 8 nodes
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
1973 = Sophie Germain prime, Leonardo prime
1975 = number of partitions of 28 with nonnegative rank
1976 = octagonal number
1979 = number of squares between 452 and 454, smallest number that is the sum of 4 positive cubes in at least 4 ways
1980 = pronic number, highly abundant number with a greater sum of proper divisors than all smaller numbers
1984 = 11111000000 in binary, nonunitary perfect number,
1985 = centered square number
1987 = 300th prime number
1988 = sum of the first 33 primes,
1990 = Stella octangula number
1991 = 11 × 181, the 46th Gullwing number, palindromic composite number with only palindromic prime factors
1999 = centered triangular number, number of regular forms in a myriagram.