Encyclopedia

1000 (number)

Natural number

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Source updated September 15, 2026

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.

01Notation

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:
- 1 × 10³ 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 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.

02Numbers in the range 1001-1999

1001 to 1099

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

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:

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

1097

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

1100 to 1199

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

1109

1109 is a Chen prime.

1113

1113 = 3 × 7 × 53. There are 1113 strict partitions 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.

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.

1200 to 1299

1200

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

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

1202

1202 = 2 × 601. There are a maximum of 1202 regions when the plane is divided by 25 ellipses.

1203

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

1204 = 2² × 7 × 43. It is the magic constant for a 7 × 7 × 7 magic cube.

1205

1205 = 5 × 241. There are 1205 partitions of 28 such that the number of odd parts is a part

1207

1207 = 17 × 71. It is a composite de Polignac number.

1208

1208 = 2³ × 151. There are 1208 strict chains of divisors starting with the superprimorial A006939(3).

1210

1210 = 2 × 5 × 11². It is an amicable number with 1184 and a Self-descriptive number.

1211

1211 = 7 × 173. It is a composite de Polignac number

1212

1212 = 2² × 3 × 101 = $\sum _{k=0}^{17}p(k)$ , where $p(k)$ is the number of partitions of $k$ .

1213

1213 is a prime number and an emirp.

1214

1214 = 2 × 607. It is a spy number and the sum of the first 39 composite numbers.

1215

1215 = 3⁵ × 5. There are 1215 edges in the hexagonal triangle T(27)

1216

1216 = 2⁶ × 19. It is a nonagonal number

1217

1217 is a super-prime and a Proth prime.

1219

1219 = 23 × 53. It is a centered triangular number and a zero of Mertens function.

1220

1220 = 2² × 5 × 61. It is a zero of Mertens function. There are 1220 binary vectors of length 16 containing no singletons.

1222

1222 = 2 × 13 × 47. It is a hexagonal pyramidal number.

1223

1223 is the 200th prime number. It is also a Sophie Germain prime and a balanced prime.

1224

1224 = 2³ × 3² × 17. There are 1224 edges in the join of two cycle graphs, both of order 34.

1225

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

1226 = 2 × 613. There are 1226 rooted identity trees with 15 nodes.

1228

1228 = 2² × 307. It is the sum of the totient function for the first 63 integers.

1229

1229 is a Sophie Germain prime and an emirp. There are 1229 primes less than 10,000.

1230

1230 = 2 × 3 × 5 × 41 = T(9, 6), the Mahonian number.

1231

1231 is a prime number and an emirp.

1232

1232 = 2⁴ × 7 × 11. There are 1232 labeled ordered set of partitions of a 7-set into odd parts.

1234

It has two distinct prime factors, 2 and 617, making it a squarefree semiprime. It is the number of independent vertex sets in a 4×4 square grid, or equivalently, the number of distinct 4×4 binary matrices in which no two adjacent elements are both equal to 1.

1240

1240 = 2³ × 5 × 31. It is a square pyramidal number.

1241

1241 = 17 × 73. It is a centered cube number and a spy number.

1243

1243 = 11 × 113. It is a composite de Polignac number.

1244

1244 = 2² × 311. There are 1244 complete partitions of 25.

1245

1245 = 3 × 5 × 83. There are 1245 labeled spanning intersecting set-systems on 5 vertices.

1247

1247 = 29 × 43. It is a pentagonal number.

1249

1249 is a prime number, an emirp, and a trimorphic number.

1257

1257 = 3 × 419. There are 1257 lattice points inside a circle of radius 20.

1259

1259 is a prime number and a highly cototient number.

1260

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 partitions of 41.

1261

1261 = 13 × 97. It is a star number and a zero of Mertens function.

1264

1264 = 2⁴ × 79. It is the sum of the first 27 primes.

1265

1265 = 5 × 11 × 23. There are 1265 rooted trees with 43 vertices in which vertices at the same level have the same degree.

1266

1266 = 2 × 3 × 211. It is a centered pentagonal number and a zero of Mertens function.

1269

1269 = 3³ × 47. Completing 11 revolutions in the Spiral of Theodorus requires 1269 triangles.

1275

1275 = 3 × 5² × 17. It is the 50th triangular number.

1276

1276 = 2² × 11 × 29. There are 1276 irredundant sets in the 25-cocktail party graph.

1277

1277 is a prime number. It is the start of a prime constellation of length 9 (a "prime nonuple").

1278

1278 = 2 × 3² × 71. There are 1278 Narayana's cows and calves after 20 years.

1279

1279 is a prime number and a Mersenne prime exponent.

1280

1280 = 2⁸ × 5. There are 1280 parts in all compositions of 9.

1281

1281 = 3 × 7 × 61. It is an octagonal number.

1283

1283 is a safe prime.

1284

1284 = 2² × 3 × 107 = 641 + 643, the sum of a twin prime pair.

1285

1285 = 5 × 257. There are 1285 free nonominoes.

1286

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

1288 = 2³ × 7 × 23. It is a heptagonal number.

1289

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

1291 is a twin prime with 1289.

1296

1296 = 2⁴ × 3⁴ = 6⁴ = 36². It is the sum of the cubes of the first eight positive integers:

1³ + 2³ + 3³ + 3³ + 4³ + 5³ + 6³ + 7³ + 8³ = 1296.

There are 1296 rectangles on a normal 8 × 8 chessboard. There are 1296 combinations of 2 alphanumeric characters.

1297

1297 is a super-prime, a pinwheel number, and a zero of Mertens function.

1300 to 1399

1300

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

1301 is a prime number and a centered square number. There are 1301 trees with 13 unlabeled nodes.

1306

1306 = 2 × 653. It is a centered triangular number.

1307

1307 is a safe prime.

1308

1308 = 2² × 3 × 109. It is the sum of the totient function for the first 65 integers.

1312

1312 = 2⁵ × 41. It is a member of the Mian-Chowla sequence.

1319

1319 is a safe prime.

1325

1325 = 5² × 53. It is a Markov number and a centered tetrahedral number.

1326

1326 = 2 × 3 × 13 × 17. It is the 51st triangular number and a hexagonal number.

1327

1327 is the smallest prime number preceding a prime gap of 34.

1328

1328 = 2⁴ × 83. It is the sum of the totient function for the first 66 integers.

1330

1330 = 2 × 5 × 7 × 19. It is a tetrahedral number. It forms a Ruth-Aaron pair with 1331 under second definition.

1331

1331 = 11³. It is a centered heptagonal number. It forms a Ruth-Aaron pair with 1330 under second definition.

1335

1335 = 3 × 5 × 89. It is a pentagonal number.

1342

1342 = 2 × 11 × 61 = $\sum _{k=1}^{40}\sigma (k)$ .

1346

1346 = 2 × 673. There are 1346 locally disjointed rooted trees with 10 nodes.

1350

1350 = 2 × 3³ × 5². It is a nonagonal number.

1361

1361 is first prime number following a prime gap of 34 and the 3rd Mills' prime. It is a centered decagonal number

1364

1364 = 2² × 11 × 31. It is a Lucas number.

1365

1365 = 3 × 5 × 7 × 13. It is a pentatope number.

1367

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

1371 = 3 × 457. It is the sum of the first 28 primes.

1377

1377 = 3⁴ × 17. It is the maximal number of pieces that can be obtained by cutting an annulus with 51 cuts

1378

1378 = 2 × 13 × 53. It is the 52nd triangular number

1379

1379 = 7 × 197. It is the magic constant of n × n normal magic square and n-queens problem for n = 14.

1380

1380 = 2² × 3 × 5 × 23. There are 1380 8-step mappings with 4 inputs.

1381

1381 is a prime number and a centered pentagonal number.

1384

1384 = 2³ × 173 = $\sum _{k=1}^{41}\sigma (k)$

1385

1385 = 5 × 277. It is an up/down number.

1387

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

1388 = 2² × 347. Because 1388 = 4 × 19² - 3 × 19 + 1, is on the x-axis of Ulams spiral.

1394

1394 = 2 × 17 × 41. It is the sum of the totient function for the first 67 integers.

1395

1395 = 3² × 5 × 19. It is a vampire number and a member of the Mian-Chowla sequence

1396

1396 = 2² × 349. It is a centered triangular number.

1399

1399 is a prime number and an emirp.

1400 to 1499

1403

1403 = 23 × 61. It is the smallest number x such that M(x) = 11, where M() is Mertens function

1404

1404 = 2² × 3² × 13. It is a heptagonal number.

1405

1405 = 5 × 281 = 26² + 27² = 7² + 8² + ... + 16². It is a centered square number

1406

1406 = 2 × 19 × 37. It is a semi-meandric number.

1409

1409 is a super-prime, a Sophie Germain prime, and a Proth prime.

1410

1410 = 2 × 3 × 5 × 47. It is the denominator of the 46th Bernoulli number

1418

1418 = 2 × 709. It is the smallest number x such that M(x) = 13, where M() is Mertens function

1425

1425 = 3 × 5² × 19. It is a self-descriptive number in base 5.

1426

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 partitions of 42.

1427

1427 is a twin prime with 1429.

1428

1428 = 2² × 3 × 7 × 17. There are 1428 complete ternary trees with 6 internal nodes or, equivalently, 18 edges.

1429

1429 is a twin prime with 1427.

1430

1430 = 2 × 5 × 11 × 13. It is a Catalan number.

1431

1431 = 3³ × 53. It is the 53rd triangular number and a hexagonal number.

1432

1432 = 2³ × 179. It is a member of the Padovan sequence.

1433

1433 is a super-prime.

1435

1435 = 5 × 7 × 41. It is a vampire number.

1436

1436 = 2² × 359. It is the discriminant of a totally real cubic field.

1439

1439 is a Sophie Germain prime and a safe prime.

1440

1440 = 2⁵ × 3² × 5. It is a highly totient number.

1441

1441 = 11 × 131. It is a star number.

1447

1447 is a super-prime number and a happy number.

1451

1451 is a Sophie Germain prime.

1452

1452 = 2² × 3 × 11². It is the first Zagreb index of the complete graph K₁₂.

1453

1453 is a Sexy prime with 1459.

1458

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

1459 is a Sexy prime with 1453 and a Pierpont prime. It is the sum of nine consecutive primes:

1459 = 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181.

1462

1462 = 2 × 17 × 43. Because 1462 = (35 - 1) × (35 + 8), it is the first Zagreb index of the wheel graph with 35 vertices

1467

1467 = 3² × 163. There are 1467 partitions of 39 with zero crank.

1469

1469 = 13 × 113. It is an octahedral number and a highly cototient number.

1470

1470 = 2 × 3 × 5 × 7². It is the sum of the totient function for the first 69 integers.

1471

1471 is a super-prime number and a centered heptagonal number.

1480

1480 = 2³ × 5 × 37. It is the sum of the first 29 primes.

1481

1481 is a Sophie Germain prime.

1485

1485 = 3³ × 5 × 11. It is the 54th triangular number.

1486

1486 = 2 × 743. There are 1486 strict solid partitions of 19.

1487

1487 is a safe prime.

1489

1489 is a prime number and a centered triangular number.

1490

1490 = 2 × 5 × 149. It is a tetranacci number.

1491

1491 = 3 × 7 × 71. It is a nonogonal number.

1492

1492 = 2² × 373. It is the discriminant of a totally real cubic field.

1493

1493 is a Stern prime.

1494

1494 = 2 × 3² × 83. It is the sum of the totient function for the first 70 integers.

1496

1496 = 2³ × 11 × 17. It is a square pyramidal number.

1499

1499 is a Sophie Germain prime and a super-prime.

1500 to 1599

1500

1500 = 2² × 3 × 5³. It is the hypotenuse of three different Pythagorean triangles.

1501

1501 = 19 × 79. It is a centered pentagonal number.

1503

1503 = 3² × 167. Completing 12 revolutions of the Spiral of Theodorus requires 1503 triangles.

1510

1510 = 2 × 5 × 151. 1510 is an untouchable number.

1511

1511 is a Sophie Germain prime and a balanced prime.

1513

1513 = 17 × 89. It is a centered square number.

1520

1520 = 2⁴ × 5 × 19. It is a pentagonal number. It forms a Ruth-Aaron pair with 1521 under the second definition.

1521

1521 = 3² × 13² = 39². It is a centered octagonal number. It forms a Ruth-Aaron pair with 1520 under the second definition.

1523

1523 is a super-prime, a safe prime, and a member of the Mian-Chowla sequence.

1525

1525 = 5² × 61. It is a heptagonal number.

1526

1526 = 2 × 7 × 109. There are 1526 conjugacy classes in the alternating group A₂₇.

1529

1529 = 11 × 139. It is a composite de Polignac number.

1530

1530 = 2 × 3² × 5 × 17. It is a vampire number.

1531

1531 is a prime number and a centered decagonal number.

1532

1532 = 2² × 383. There are 1532 series-parallel networks with 9 unlabeled edges,

1535

1535 = 5 × 307. It is a Thabit number.

1537

1537 = 29 × 53. It is a Keith number.

1539

1539 = 3⁴ × 19. A maximum of 1539 pieces can be obtained by cutting an annulus with 54 cuts.

1540

1540 = 2² × 5 × 7 × 11. It is the 55th triangular number, a hexagonal number, a decagonal number, and a tetrahedral number.

1541

1541 = 23 × 67. It is an octagonal number.

1549

1549 is a de Polignac prime.

1557

1557 = 3² × 173. There are 1557 graphs with 8 nodes and 13 edges.

1559

1559 is a Sophie Germain prime.

1561

1561 = 7 × 223. It is a centered octahedral number.

1564

1564 = 2² × 17 × 23. It is the sum of the totient function for the first 71 integers.

1572

1572 = 2² × 3 × 131. It is a member of the Mian-Chowla sequence.

1573

1573 = 11² × 13. It is the discriminant of a totally real cubic field.

1583

1583 is a Sophie Germain prime.

1585

1585 = 5 × 307. It is a centered triangular number.

1588

1588 = 2² × 397. It is the sum of the totient function for the first 72 integers.

1589

1589 = 7 × 227. It is a composite de Polignac number.

1593

1593 = 3³ × 59. It is the sum of the first 30 primes.

1594

1594 = 2 × 797. It is the minimal cost of a maximum height Huffman tree of size 17.

1596

1596 = 2² × 3 × 7 × 19. It is the 56th triangular number.

1597

1597 is a super-prime, a Fibonacci prime, a Markov prime, and an emirp.

1600 to 1699

1601

1601 is a Sophie Germain prime and a Proth prime.

1607, 1609, and 1613

1607, 1609, and 1613 form a prime triple.

1617

1617 = 3 × 7² × 11. It is a pentagonal number.

1618

1618 = 2 × 809. It is a centered heptagonal number.

1619

1619 is a safe prime.

1621

1621 is a super-prime.

1624

1624 = 2³ × 7 × 29. There are 1624 squares in the Aztec diamond of order 28.

1625

1625 = 5³ × 13. It is a centered square number.

1626

1626 = 2 × 3 × 271. It is a centered pentagonal number.

1633

1633 = 23 × 71. It is a star number.

1634

1634 = 2 × 19 × 43. It is the smallest four-digit Narcissistic number in base 10.

1637

1637 is a prime island: it is the smallest prime whose adjacent primes are exactly 30 apart.

1638

1638 = 2 × 3² × 7 × 13. It is a harmonic divisor number.

1639

1639 = 11 × 149. It is a nonagonal number.

1646

1646 = 2 × 823. There are 1646 graphs with 8 nodes and 14 edges.

1649

1649 = 17 × 97. It is a highly cototient number and a Leyland number using 4 and 5: 1649 = 4⁵ + 5⁴.

1651

1651 = 13 × 127. It is a heptagonal number.

1653

1653 = 3 × 19 × 29. It is the 57th triangular number and a hexagonal number.

1657

1657 is a cuban prime.

1660

1660 = 2² × 5 × 83. It is the sum of the totient function for the first 73 integers.

1665

1665 = 3² × 5 × 37. It is a centered tetrahedral number.

1669

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

1680 = 2⁴ × 3 × 5 × 7. It is the 17th highly composite number.

1681

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

1682 and 1683 form a Ruth-Aaron pair under the first definition.

1684

1684 = 2² × 421. It is a centered triangular number.

1691

1691 = 19 × 89. It is a strobogrammatic number.

1695

1695 = 3 × 5 × 113. It is the magic constant of n × n normal magic square and the n-queens problem for n = 15.

1696

1696 = 2⁵ × 53. It is the sum of the totient function for the first 74 integers.

1700 to 1799

1705

1705 = 5 × 11 × 13. It is a tribonacci number.

1710

1710 = 2 × 3² × 5 × 19. A maximum of 1710 pieces can be obtained by cutting an annulus 57 times.

1711

1711 = 29 × 59. It is the 58th triangular number and a centered decagonal number.

1717

1717 = 17 × 101. It is a pentagonal number.

1719

1719 = 3² × 131. it is a composite de Polignac number.

1720

1720 = 2³ × 5 × 43. It is the sum of the first 31 primes.

1721

1721 is a twin prime with 1723.

1722

1722 = 2 × 3 × 7 × 41. It is a Giuga number and a pronic number.

1723

1723 is a twin prime with 1721. It is also a super-prime.

1728

1729

1733

1733 is a Sophie Germain prime. It is palindromic in bases 3, 18, and 19.

1736

1736 = 2³ × 7 × 31. It is the sum of the totient function for the first 75 integers.

1740

1740 = 2² × 3 × 5 × 29. There are 1740 squares in the Aztec diamond of order 29.

1741

1741 is a super-prime and a centered square number.

1747

1747 is a balanced prime.

1750

1750 = 2 × 5³ × 7. It is the hypotenuse of three different Pythagorean triangles with integer side lengths.

1753

1753 is a balanced prime.

1756

1756 = 2² × 439. It is a centered pentagonal number.

1757

1757 = 7 × 251. Completing 13 revolutions around the Spiral of Theodorus requires 1757 triangles.

1759

1759 is a de Polignac prime.

1765

1765 = 5 × 353. There are 1765 planar partitions of 15.

1769

1769 = 29 × 61. A maximum of 1769 pieces can be obtained by cutting an annulus with 58 times.

1770

1770 = 2 × 3 × 59. It is the 59th triangular number and a hexagonal number.

1771

1771 = 7 × 11 × 23. It is a tetrahedral number.

1772

1772 = 2² × 443. It is a centered heptagonal number and the sum of the totient function for the first 76 integers.

1776

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

1782 = 2 × 3⁴ × 11. It is a heptagonal number.

1783

1783 is a de Polignac prime.

1785

1785 = 3 × 5 × 7 × 17. It is a square pyramidal number.

1786

1786 = 2 × 19 × 47. It is a centered triangular number.

1787

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

1792 = 2⁸ × 7. It is a Granville number.

1794

1794 = 2 × 3 × 13 × 23. It is a nonagonal number.

1800 to 1899

1801

1801 is a cuban prime. It is the sum of five consecutive primes (349 + 353 + 359 + 367 + 373) and nine consecutive primes 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227).

1806

1806 = 2 × 3 × 301. It is a pronic number, a primary pseudoperfect number, and a Schröder number. It is the only number n such that the denominator of the nth Bernoulli number is n.

1807

1807 = 13 × 139. It is the fifth term of Sylvester's sequence.

1811

1811 is a Sophie Germain prime.

1820

1820 = 2² × 5 × 7 × 13. It is a pentagonal number and a pentatope number.

1821

1821 = 3 × 607. It is a member of the Mian-Chowla sequence.

1823

1823 is a super-prime and a safe prime.

1825

1825 = 5² × 73. It is an octagonal number.

1827

1827 = 3² × 7 × 29. It is a vampire number.

1828

1828 = 2² × 457. It is a meandric number as well as an open meandric number.

1829

1829 = 31 × 59. composite de Polignac number.

1830

1830 = 2 × 3 × 5 × 61. It is the 60th triangular number.

1831

1831 is the smallest prime number with a gap of exactly 16 to the next prime, 1847.

1834

1834 = 2 × 7 × 131. It is an octahedral number.

1837

1837 = 11 × 167. It is a star number.

1841

1841 = 7 × 263. It is the solution to the postage stamp problem with 3 denominations and 29 stamps.

1847

1847 is a super-prime.

1859

1859 = 11 × 13². It is a composite de Polignac number.

1861

1861 is a prime number and a centered square number.

1862 and 1863

1862 and 1863 form a Ruth-Aaron pair under the second definition.

1867

1867 is a prime de Polignac number.

1870

1870 = 2 × 5 × 11 × 17. It is a decagonal number.

1871, 1873, 1877, and 1879

1871, 1873, 1877, and 1879 form a prime quadruple.

There are 1873 Narayana's cows and calves after 21 years.

1880

1880 = 2³ × 5 × 47. It is the 10th element of the self convolution of Lucas numbers.

1882

1882 = 2 × 941. There are 1882 linearly separable Boolean functions in 4 variables.

1889

1889 is a Sophie Germain prime and a highly cototient number.

1891

1891 = 31 × 61. It is the 61st triangular number, a centered triangular number a hexagonal number, a centered pentagonal number, and the sum of 5 consecutive primes: 1891 = 367 + 373 + 379 + 383 + 389.

1892

1892 = 2² × 11 × 43. It is a pronic number.

1896

1896 = 2³ × 3 × 79. It is a member of the Mian-Chowla sequence.

1897

1897 = 7 × 271. It is a member of the Padovan sequence.

1900 to 1999

1901

1901 is a Sophie Germain prime and a centered decagonal number.

1905

1905 = 3 × 5 × 127. It is a Fermat pseudoprime.

1907

1907 is a safe prime and a balanced prime.

1909

1909 = 23 × 83. It is a hyperperfect number.

1913

1913 is a super-prime.

1918

1918 = 2 × 7 × 137. It is a heptagonal number.

1926

1926 = 2 × 3² × 107. It is a pentagonal number.

1931

1931 is a Sophie Germain prime.

1933

1933 is a prime number and a centered heptagonal number.

1951

1951 is a cuban prime.

1953

1953 = 3² × 7 × 31. It is the 62nd triangular number.

1956

1956 = 2² × 3 × 163. It is a nonagonal number.

1969

1969 = 11 × 179. It is the only number less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize

1973

1973 is a Sophie Germain prime and a Leonardo prime.

1976

1976 = 2³ × 13 × 19. It is an octagonal number.

1980

1980 = 2² × 3² × 5 × 11. It is a pronic number and a highly abundant number, and it also has a greater aliquot sum than any smaller number.

1985

1985 = 5 × 397. It is a centered square number.

1987

1987 is the first number of a sexy prime triplet (1987, 1993, 1999). It is a lucky number and therefore also a lucky prime.

1990

1990 = 2 × 5 × 199. It is a Stella octangula number.

1993

1993 forms a prime triplet with 1987 and 1999.

1999

1999 is a prime number that forms a prime triplet with 1987 and 1993. It is also a centered triangular number. There are 1999 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

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Sources and credits

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