1000 (number)

1001

1004

1004 = 2² × 251. It is a heptanacci number.

1009

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

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.

1013

1013 is a prime number, a Sophie Germain prime, and a centered square number,

1016

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

1019 is a Sophie Germain prime, a safe prime, and a Chen prime.

1021

1021 is a Lucky prime and a twin prime with 1019.

1023

1024

1025

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

1028 = 2² × 257. It is sum of totient function for first 58 integers.

1029

There are 1029 primes <= 2¹³.

1031

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

1033 is a prime number and an emirp. It forms a twin prime pair with 1031.

1035

1035 = 3² × 5 × 23. It is a hexagonal number and the 45th triangular number.

1039

1039 is a Chen prime and a Lucky prime. There are 1039 partitions of 30 that do not contain 1 as a part.

1040

1040 = 2⁴ × 5 × 13. There are 1040 pieces that could be seen in a 6 × 6 × 6 × 6 Rubik's Tesseract.

1046

1046 = 2 × 523. It is a coefficient of f(q), the 3rd order mock theta function.

1049

1049 is a prime number, a Sophie Germain prime, a highly cototient number, and a Chen prime.

1051

1051 is a prime number, a centered pentagonal number, and a centered decagonal number.

1056

1056 = 2⁵ × 3 × 11. It is a pronic number.

1060

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

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

1063 is a prime number, a super-prime, a twin prime with 1061, and the sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167)

1069

1069 is a prime number and an emirp.

1076

1076 = 2² × 269. There are 1076 strict trees weight 11.

1078

1078 = 2 × 7² × 11. It is an Euler transform of negative integers.

1080

1080 = 2³ × 3³ × 5. It is a pentagonal number and a largely composite number.

1081

1081 = 23 × 47. It is the 46th triangular number and a member of Padovan sequence.

1086

1086 = 2 × 3 × 181. It is a Smith number and the sum of totient function for the first 59 integers.

1087

1087 is a prime number, a super-prime, a cousin prime, and a lucky prime.

1089

1089 is a square number (33 squared), a nonagonal number, a 32-gonal number, a 364-gonal number, and a centered octagonal number. 1089 is the first nontrivial decimal reverse-divisible number: multiplying 1089 by 9 gives 9801, the reversal of its digits.

1091

1091 is a prime number, a cousin prime, and a twin prime with 1093.

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:

${\displaystyle 1093=1111111_{3}=3^{6}+3^{5}+3^{4}+3^{3}+3^{2}+3^{1}+3^{0}={\frac {3^{7}-1}{2}}\,.}$

1097

1097 is a prime number, an emirp, and a Chen prime.

1102

1102 = 2 × 19 × 29. It is the sum of the totient function for the first 60 integers.

1103

1103 is a prime number, a Sophie Germain prime, and a balanced prime.

1104

1104 = 2⁴ × 3 × 23. It is a Keith number

1105

1105 is the smallest positive integer that is a sum of two positive squares in exactly four different ways, a property that can be connected (via the sum of two squares theorem) to its factorization 5 × 13 × 17 as the product of the three smallest prime numbers that are congruent to 1 modulo 4. It is also the second-smallest Carmichael number, after 561, one of the first four Carmichael numbers identified by R. D. Carmichael in his 1910 paper introducing this concept. It is also a Fermat pseudoprime.

It is a member of the Moser–de Bruijn sequence of sums of distinct powers of four.

1109

1109 is a Chen prime.

1113

1113 = 3 × 7 × 53. There are 1113 strict partions of 40.

1117

1117 is a Chen prime. There are 1117 diagonally symmetric polyominoes with 16 cells.

1118

1118 = 2 × 13 × 43. There are 1118 unimodular 2 × 2 matrices having all terms in {0,1,...,21}.

1119

1119 = 3 × 373. There are 1119 bipartite graphs with 9 nodes.

1122

1122 = 2 × 3 × 11 × 17. It is a pronic number.

1123

1123 is a balanced prime.

1126

1126 = 2 × 563. There are 1126 2 × 2 non-singular integer matrices with entries from {0, 1, 2, 3, 4, 5}.

1127

1127 = 7² × 23. It is the maximum number of pieces that can be obtained by cutting an annulus with 46 cuts.

1128

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

1152 = 2⁷ × 3². It is a highly totient number, a 3-smooth number, and an Achilles number.

1153

1153 is a super-prime and a Proth prime.

1159

1159 = 19 × 61. It is a centered octahedral number and a member of the Mian–Chowla sequence.

1160

1160 = 2³ × 5 × 29. It is an octagonal number.

1161

1161 = 3³ × 43. It is the sum of the first twenty-six primes.

1162

1162 = 2 × 7 × 83. It is the sum of the totient function for the first 61 integers and a pentagonal number.

1163

1163 is a Chen prime.

1164

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

1169 = 7 × 167. It is a highly cototient number

1171

1171 is a super-prime.^[source?]

1173

1173 = 3 × 17 × 23. There are 1173 simple triangulations on a plane with 9 nodes.

1174

1174 = 2 × 587. There are 1174 widely totally strongly normal compositions of 16. (sequence A332337 in the OEIS).

1175

1175 = 5² × 47. It is the maximum number of pieces that can be obtained by cutting an annulus with 47 cuts.

1176

1176 = 2³ × 3 × 7². It is the 48th triangular number.

1178

1178 = 2 × 19 × 31. There are 1178 surface points on a cube with edge-length 15.

1179

1179 = 3² × 131. There are 1179 different permanents of binary 7 by 7 matrices.

1182

1182 = 2 × 3 × 197. There are 1182 necklaces possible with 14 beads of 2 colors (that cannot be turned over).

1184

1184 = 2⁵ × 37. It is an amicable number with 1210.

1186

1186 = 2 × 593. There are 1186 diagonally symmetric polyominoes with 15 cells.

1187

1187 is a safe prime, a Stern prime, a balanced prime, and a Chen prime.

1190

1190 = 2 × 5 × 7 × 17. It is a pronic number. Building a 28-tier house of cards requires 1190 cards.

1191

1191 = 3 × 397 = 35² - 35 + 1 = H₃₅, the 35th Hogben number.

1192

1192 = 2³ × 149. It is the sum of the totient function for the first 62 integers.

1193

1193 is a Chen prime.

4¹¹⁹³ - 3¹¹⁹³ is prime.

1198

1198 = 2 × 599. It is a centered heptagonal number.

1201

1201 is a super-prime, a centered square number, and a centered decagonal number.