# every number has its own significance.....

**From:** Andy (*andylee_at_home.com*)

**Date:** 11/12/05

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Date: Fri, 11 Nov 2005 17:02:42 -0600

every number has its own significance.....................

0 is the additive identity.

1 is the multiplicative identity.

2 is the only even prime.

3 is the number of spatial dimensions we live in.

4 is the smallest number of colors sufficient to color all planar

maps.

5 is the number of Platonic solids.

6 is the smallest perfect number.

7 is the smallest number of integer-sided rectangles that tile a

rectangle so that no 2 rectangles share a common length.

8 is the largest cube in the Fibonacci sequence.

9 is the maximum number of cubes that are needed to sum to any

positive integer.

10 is the base of our number system.

11 is the largest known multiplicative persistence.

12 is the smallest abundant number.

13 is the number of Archimedian solids.

14 is the smallest number n with the property that there are no

numbers relatively prime to n smaller numbers.

15 is the smallest composite number n with the property that there is

only one group of order n.

16 is the only number of the form xy=yx with x and y different

integers.

17 is the number of wallpaper groups.

18 is the only number that is twice the sum of its digits.

19 is the maximum number of 4th powers needed to sum to any number.

20 is the number of rooted trees with 6 vertices.

21 is the smallest number of distinct squares needed to tile a square.

22 is the number of partitions of 8.

23 is the smallest number of integer-sided boxes that tile a box so

that no two boxes share a common length.

24 is the largest number divisible by all numbers less than its square

root.

25 is the smallest square that can be written as a sum of 2 squares.

26 is the only number to be directly between a square and a cube.

27 is the largest number that is the sum of the digits of its cube.

28 is the 2nd perfect number.

29 is the 7th Lucas number.

30 is the largest number with the property that all smaller numbers

relatively prime to it are prime.

31 is a Mersenne prime.

32 is the smallest 5th power (besides 1).

33 is the largest number that is not a sum of distinct triangular

numbers.

34 is the smallest number with the property that it and its neighbors

have the same number of divisors.

35 is the number of hexominoes.

36 is the smallest number (besides 1) which is both square and

triangular.

37 is the maximum number of 5th powers needed to sum to any number.

38 is the last Roman numeral when written lexicographically.

39 is the smallest number which has 3 different partitions into 3

parts with the same product.

40 is the only number whose letters are in alphabetical order.

41 is the smallest number that is not of the form |2x - 3y|.

42 is the 5th Catalan number.

43 is the number of sided 7-iamonds.

44 is the number of derangements of 5 items.

45 is a Kaprekar number.

46 is the number of different arrangements (up to rotation and

reflection) of 9 non-attacking queens on a 9x9 chessboard.

47 is the largest number of cubes that cannot tile a cube.

48 is the smallest number with 10 divisors.

49 is the smallest number with the property that it and its neighbors

are squareful.

50 is the smallest number that can be written as the sum of of 2

squares in 2 ways.

51 is the 6th Motzkin number.

52 is the 5th Bell number.

53 is the only two digit number that is reversed in hexadecimal.

54 is the smallest number that can be written as the sum of 3 squares

in 3 ways.

55 is the largest triangular number in the Fibonacci sequence.

56 is the number of reduced 5 x 5 Latin squares.

57 = 111 in base 7.

58 is the number of commutative semigroups of order 4.

59 is the smallest number whose 4th power is of the form a4+b4-c4.

60 is the smallest number divisible by 1 through 6.

61 is the 6th Euler number.

62 is the smallest number that can be written as the sum of of 3

distinct squares in 2 ways.

63 is the number of partially ordered sets of 5 elements.

64 is the smallest number with 7 divisors.

65 is the smallest number that becomes square if its reverse is either

added to or subtracted from it.

66 is the number of 8-iamonds.

67 is the smallest number which is palindromic in bases 5 and 6.

68 is the last 2-digit string to appear in the decimal expansion of .

69 has the property that n2 and n3 together contain each digit once.

70 is the smallest abundant number that is not the sum of some subset

of its divisors.

71 divides the sum of the primes less than it.

72 is the maximum number of spheres that can touch another sphere in a

lattice packing in 6 dimensions.

73 is the smallest number (besides 1) which is one less than twice its

reverse.

74 is the number of different non-Hamiltonian polyhedra with minimum

number of vertices.

75 is the number of orderings of 4 objects with ties allowed.

76 is an automorphic number.

77 is the largest number that cannot be written as a sum of distinct

numbers whose reciprocals sum to 1.

78 is the smallest number that can be written as the sum of of 4

distinct squares in 3 ways.

79 is a permutable prime.

80 is the smallest number n where n and n+1 are both products of 4 or

more primes.

81 is the square of the sum of its digits.

82 is the number of 6-hexes.

83 is the number of zero-less pandigital squares.

84 is the largest order of a permutation of 14 elements.

85 is the largest n for which 12+22+32+...+n2 = 1+2+3+...+m has a

solution.

86 = 222 in base 6.

87 is the sum of the squares of the first 4 primes.

88 is the only number known whose square has no isolated digits.

89 = 81 + 92

90 is the number of degrees in a right angle.

91 is the smallest pseudoprime in base 3.

92 is the number of different arrangements of 8 non-attacking queens

on an 8x8 chessboard.

93 = 333 in base 5.

94 is a Smith number.

95 is the number of planar partitions of 10.

96 is the smallest number that can be written as the difference of 2

squares in 4 ways.

97 is the smallest number with the property that its first 3 multiples

contain the digit 9.

98 is the smallest number with the property that its first 5 multiples

contain the digit 9.

99 is a Kaprekar number.

100 is the smallest square which is also the sum of 4 consecutive

cubes.

101 is the number of partitions of 13.

102 is the smallest number with three different digits.

103 has the property that placing the last digit first gives 1 more

than triple it.

104 is the smallest known number of unit line segments that can exist

in the plane, 4 touching at every vertex.

105 is the largest number n known with the property that n - 2k is

prime for k>1.

106 is the number of trees with 10 vertices.

107 is the exponent of a Mersenne prime.

108 is 3 hyperfactorial.

109 is the smallest number which is palindromic in bases 5 and 9.

110 is the smallest number that is the product of two different

substrings.

111 is the smallest possible magic constant of a 3 x 3 magic square of

distinct primes.

112 is the side of the smallest square that can be tiled with distinct

integer-sided squares.

113 is a permutable prime.

114 = 222 in base 7.

115 is the number of rooted trees with 8 vertices.

116 is a value of n for which n!+1 is prime.

117 is the smallest possible value of the longest edge in a Heronian

Tetrahedron.

118 is the smallest number that has 4 different partitions into 3

parts with the same product.

119 is the smallest number n where either n or n+1 is divisible by the

numbers from 1 to 8.

120 is the smallest number to appear 6 times in Pascal's triangle.

121 is the only square known of the form 1+p+p2+p3+p4, where p is

prime.

122 is the smallest number n>1 so that n concatenated with n-1 0's

concatenated with the reverse of n is prime.

123 is the 10th Lucas number.

124 is the smallest number with the property that its first 3

multiples contain the digit 2.

125 is the only number known that contains all its proper divisors as

proper substrings.

126 = 9C4.

127 is a Mersenne prime.

128 is the largest number which is not the sum of distinct squares.

129 is the smallest number that can be written as the sum of 3 squares

in 4 ways.

130 is the number of functions from 6 unlabeled points to themselves.

131 is a permutable prime.

132 is the smallest number which is the sum of all of the 2-digit

numbers that can be formed with its digits.

133 is the smallest number n for which the sum of the proper divisors

of n divides phi(n).

134 = 8C1 + 8C3 + 8C4.

135 = 11 + 32 + 53.

136 is the sum of the cubes of the digits of the sum of the cubes of

its digits.

137 is the smallest prime with 3 distinct digits that remains prime if

one of its digits is removed.

138 is the smallest possible product of 3 primes, one of which is the

concatenation of the other two.

139 is the number of unlabeled topologies with 5 elements.

140 is the smallest harmonic divisor number.

141 is a Cullen number.

142 is the number of planar graphs with 6 vertices.

143 is the smallest quasi-Carmichael number in base 8.

144 is the largest square in the Fibonacci sequence.

145 = 1! + 4! + 5!

146 = 222 in base 8.

147 is the number of sided 6-hexes.

148 is the number of perfect graphs with 6 vertices.

149 is the concatenation of the first 3 positive squares

150 is the smallest n for which n + n times the nth prime is square.

151 is a palindromic prime.

152 ???

153 = 13 + 53 + 33.

154 is the smallest number which is palindromic in bases 6, 8, and 9.

155 is the sum of the primes between its smallest and largest prime

factor.

156 is the number of graphs with 6 vertices.

157 is the largest number known whose square contains the same digits

as its successor.

158 is the number of planar partitions of 11.

159 is the number of isomers of C11H24.

160 is the number of 9-iamonds.

161 is a hexagonal pyramidal number.

162 is the smallest number that can be written as the sum of of 4

positive squares in 9 ways.

163 is the largest Heegner Number.

164 is the smallest number which is the concatenation of squares in

two different ways.

165 = 11C3.

166 is the number of monotone Boolean functions of 4 variables.

167 ???

168 is the size of the smallest non-cyclic simple group which is not

an alternating group.

169 is a square whose digits are non-decreasing.

170 is the smallest number n for which phi(n) and sigma(n) are both

square.

171 is a palindromic triangular number.

172 = 444 in base 6.

173 ???

174 is the smallest number that can be written as the sum of of 4

positive distinct squares in 6 ways.

175 = 11 + 72 + 53.

176 is an octagonal pentagonal number.

177 is the number of graphs with 7 edges.

178 has a cube with the same digits as another cube.

179 ???

180 is the total number of degrees in a triangle.

181 is a strobogrammatic prime.

182 is the number of connected bipartite graphs with 8 vertices.

183 is the smallest number n so that n concatenated with n+1 is

square.

184 is a Kaprekar constant in base 3.

185 ???

186 is the number of degree 11 irreducible polynomials over GF(2).

187 is the smallest quasi-Carmichael number in base 7.

188 is the number of semigroups of order 4.

189 is a Kaprekar constant in base 2.

190 is the largest number with the property that it and its ditinct

prime factors are palindromic in Roman numerals.

191 is a palindromic prime.

192 is the smallest number with 14 divisors.

193 is the only known odd prime n for which 2 is not a primitive root

of 4n2+1.

194 is the smallest number that can be written as the sum of 3 squares

in 5 ways.

195 is the smallest value of n such that 2nCn is divisible by n2.

196 is the smallest number that is not known to reach a palindrome

when repeatedly added to its reverse.

197 is a Keith number.

198 = 11 + 99 + 88.

199 is the 11th Lucas number.

200 is the smallest number which can not be made prime by changing one

of its digits.

201 is a Kaprekar constant in base 4.

202 ???

203 is the 6th Bell number.

204 is the square root of a triangular number.

205 is the largest number which can not be writen as the sum of

distinct primes of the form 6n+1.

206 is the smallest number that can be written as the sum of of 3

positive distinct squares in 5 ways.

207 has a 4th power where the first half of the digits are a

permutation of the last half of the digits.

208 ???

209 is the smallest quasi-Carmichael number in base 9.

210 is the product of the first 4 primes.

211 is the smallest number whose reciprocal has period 30.

212 has a square with 4/5 of the digits are the same.

213 is a number whose product of digits is equal to its sum of digits.

214 ???

215 = 555 in base 6.

216 is the smallest cube that can be written as the sum of 3 cubes.

217 is a Kaprekar constant in base 2.

218 is the number of digraphs with 4 vertices.

219 is the number of space groups, not including handedness.

220 is the smallest amicable number.

221 is the number of Hamiltonian planar graphs with 7 vertices.

222 is the number of lattices on 10 unlabeled nodes.

223 is the smallest prime which will nor remain prime if one of its

digits is changed.

224 ???

225 is an octagonal square number.

226 ???

227 is the number of connected planar graphs with 8 edges.

228 = 444 in base 7.

229 is the smallest prime that remains prime when added to its

reverse.

230 is the number of space groups, including handedness.

231 is the number of partitions of 16.

232 is the number of 7x7 symmetric permutation matrices.

233 is the smallest number with the property that it and its neighbors

can be written as a sum of 2 squares.

234 ???

235 is the number of trees with 11 vertices.

236 is the number of Hamiltonian circuits of a 4x8 rectangle.

237 is the smallest number with the property that its first 3

multiples contain the digit 7.

238 ???

239 is the largest number that cannot be written as a sum of 8 or

fewer cubes.

240 is the smallest number with 20 divisors.

241 ???

242 is the smallest number n where n through n+3 all have the same

number of divisors.

243 = 35.

244 is the smallest number (besides 2) that can be written as the sum

of 2 squares or the sum of 2 5th powers.

245 is a stella octangula number.

246 = 9C2 + 9C4 + 9C6.

247 is the smallest possible difference between two integers that

together contain each digit exactly once.

248 is the smallest number n>1 for which the arithmetic, geometric,

and harmonic means of phi(n) and sigma(n) are all integers.

249 ???

250 ???

251 is the smallest number that can be written as the sum of 3 cubes

in 2 ways.

252 is the 5th central binomial coefficient.

253 is the smallest non-trivial triangular star number.

254 is the smallest composite number all of whose divisors (except 1)

contain the digit 2.

255 = 11111111 in base 2.

256 is the smallest 8th power (besides 1).

257 is a Fermat prime.

258 ???

259 = 1111 in base 6.

260 ???

261 is the number of essentially different ways to dissect a 16-gon

into 7 quadrilaterals.

262 is the 9th meandric number.

263 is the largest known prime whose square is strobogrammatic.

264 is the largest known number whose square is undulating.

265 is the number of derangements of 6 items.

266 is the Stirling number of the second kind S(8,6).

267 is the number of planar partitions of 12.

268 is the smallest number whose product of digits is 6 times the sum

of its digits.

269 ???

270 is a harmonic divisor number.

271 is the smallest prime p so that p-1 and p+1 are divisible by

cubes.

272 is the 7th Euler number.

273 = 333 in base 9.

274 is the Stirling number of the first kind s(6,2).

275 ???

276 is the sum of the first 3 5th powers.

277 ???

278 ???

279 is the maximum number of 8th powers needed to sum to any number.

280 ???

281 ???

282 is the sum of its proper divisors that contain the digit 4.

283 = 25 + 8 + 35.

284 is an amicable number.

285 is the number of binary rooted trees with 13 vertices.

286 is the number of rooted trees with 9 vertices.

287 ???

288 is the smallest non-palindrome non-square that when multiplied by

its reverse is a square.

289 is a square whose digits are non-decreasing.

290 ???

291 is the number of functional graphs on 8 vertices.

292 is the number of ways to make change for a dollar.

293 ???

294 ???

295 ???

296 ???

297 is a Kaprekar number.

298 ???

299 ???

300 is the largest possible score in bowling

301 is a 6-hyperperfect number.

302 is the number of acyclic digraphs with 5 vertices.

303 has a cube that is a concatenation of other cubes.

307 is a non-palindrome with a palindromic square.

308 is a heptagonal pyramidal number.

309 is smallest value of n for which sigma(n-1) + sigma(n+1) =

sigma(2n).

311 is a permutable prime.

312 = 2222 in base 5.

313 is a palindromic prime.

314 is the smallest number that can be written as the sum of of 3

positive distinct squares in 6 ways.

315 = (4+3)(4+1)(4+5).

317 is a value of n for which one less than the product of the first n

primes is prime.

318 is the number of unlabeled partially ordered sets of 6 elements.

319 is the smallest number with the property that the partition with

the largest product does not have a maximum number of parts.

320 is the maximum determinant of a 10 x 10 matrix of 0's and 1's.

321 is a number whose product of digits is equal to its sum of digits.

322 is the 12th Lucas number.

323 is the product of twin primes.

325 is a 3-hyperperfect number.

327 and its double and triple together contain every digit from 1-9

exactly once.

330 = 11C4.

333 is the number of 7-hexes.

335 is the number of degree 12 irreducible polynomials over GF(2).

336 = 8P3.

337 is a permutable prime.

340 is a value of n for which n!+1 is prime.

341 is the smallest pseudoprime in base 2.

342 = 666 in base 7.

343 = (3+4)3.

344 is an octahedral number.

345 is half again as large as the sum of its proper divisors.

350 is the Stirling number of the second kind S(7,4).

351 is the smallest number n where n, n+1, and n+2 are all products of

4 or more primes.

352 is the number of different arrangements of 9 non-attacking queens

on an 9x9 chessboard.

353 is the smallest number whose 4th power can be written as the sum

of 4 4th powers.

354 is the sum of the first 4 4th powers.

355 is the number of labeled topologies with 4 elements.

360 is the number of degrees in a circle.

364 = 14C3.

365 is the smallest number that can be written as a sum of consecutive

squares in more than 1 way.

366 is the number of days in a leap year.

367 is the largest number whose square has strictly increasing digits.

369 is the number of octominoes.

370 = 33 + 73 + 03.

371 = 33 + 73 + 13.

372 is a hexagonal pyramidal number.

373 is a permutable prime.

374 is the smallest number that can be written as the sum of 3 squares

in 8 ways.

375 is a truncated tetrahedral number.

376 is an automorphic number.

377 is the 14th Fibonacci number.

379 is a value of n for which one more than the product of the first n

primes is prime.

381 is a Kaprekar constant in base 2.

382 is the smallest number n with sigma(n) = sigma(n+3).

383 is the number of Hamiltonian graphs with 7 vertices.

384 = 8!!.

385 is the number of partitions of 18.

392 is a Kaprekar constant in base 5.

399 is a value of n for which n!+1 is prime.

400 = 1111 in base 7.

401 is the number of connected planar Eulerian graphs with 9 vertices.

403 is the product of two primes which are reverses of each other.

405 is a pentagonal pyramidal number.

407 = 43 + 03 + 73.

410 is the smallest number that can written as the sum of 2 distinct

primes in 2 ways.

420 is the smallest number divisible by 1 through 7.

426 is a stella octangula number.

427 is a value of n for which n!+1 is prime.

428 has the property that its square is the concatenation of two

consecutive numbers.

429 is the 7th Catalan number.

432 = (4) (3)3 (2)2.

434 is the smallest composite value of n for which sigma(n) + 2 =

sigma(n+2).

438 = 666 in base 8.

439 is the smallest prime where inserting the same digit between every

pair of digits never yields another prime.

441 is the smallest square which is the sum of 6 consecutive cubes.

442 is the number of planar partitions of 13.

444 is the largest known n for which there is a unique integer

solution to a1+...+an=(a1)...(an).

446 is the smallest number that can be written as the sum of 3

distinct squares in 8 ways.

448 is the number of 10-iamonds.

450 = (5+4)(5+5)(5+0).

451 is the smallest number whose reciprocal has period 10.

454 is the largest number known that cannot be written as a sum of 7

or fewer cubes.

455 = 15C3.

456 is the number of tournaments with 7 vertices.

461 = 444 + 6 + 11.

462 = 11C5.

465 is a Kaprekar constant in base 2.

468 = 3333 in base 5.

469 is the largest known value of n for which n!-1 is prime.

471 is the smallest number with the property that its first 4

multiples contain the digit 4.

475 has a square that is composed of overlapping squares of smaller

numbers.

480 is the smallest number which can be written as the difference of 2

squares in 8 ways.

483 is the last 3-digit string in the decimal expansion of .

484 is a palindromic square number.

487 is the number of Hadamard matrices of order 28.

489 is an octahedral number.

490 is the number of partitions of 19.

495 is the Kaprekar constant for 3-digit numbers.

496 is the 3rd perfect number.

497 is the number of graphs with 8 edges.

499 is the smallest number with the property that its first 12

multiples contain the digit 9.

501 is the number of partitions of 5 items into ordered lists.

503 is the smallest prime which is the sum of the cubes of the first

few primes.

504 = 9P3.

505 = 10C5 + 10C0 + 10C5.

510 is the number of binary rooted trees with 14 vertices.

511 = 111111111 in base 2.

512 is the cube of the sum of its digits.

518 = 51 + 12 + 83.

521 is the 13th Lucas number.

525 is a hexagonal pyramidal number.

527 is the smallest number n for which there do not exist 4 smaller

numbers a1 through a4 so that a1! a2! a3! a4! n! is square.

528 is the sum of its proper divisors that contain the digit 6.

531 is the smallest number with the property that its first 4

multiples contain the digit 1.

535 is a palindrome whose phi(n) is also palindromic.

536 is the number of solutions of the stomachion puzzle.

538 is the 10th meandric number.

540 is divisible by its reverse.

541 is the number of orderings of 5 objects with ties allowed.

546 undulates in bases 3, 4, and 5.

548 is the maximum number of 9th powers needed to sum to any number.

550 is a pentagonal pyramidal number.

551 is the number of trees with 12 vertices.

552 is the number of prime knots with 11 crossings.

554 is the number of self-dual planar graphs with 20 edges.

555 is a repdigit.

559 is a centered cube number.

560 = 16C3.

561 is the smallest Carmichael number.

563 is the largest known Wilson prime.

567 has the property that it and its square together use the digits

1-9 once.

568 is the smallest number whose 7th power can be written as the sum

of 7 7th powers.

570 is the product of all the prime palindromic Roman numerals.

572 is the smallest number which has equal numbers of every digit in

bases 2 and 3.

573 has the property that its square is the concatenation of two

consecutive numbers.

575 is a palindrome that is one less than a square.

576 is the number of 4 x 4 Latin squares.

582 is the number of antisymmetric relations on a 5 element set.

583 is the smallest number whose reciprocal has period 26.

585 = 1111 in base 8.

586 is the smallest number that appears in its factorial 6 times.

587 is the smallest number whose sum of digits is larger than that of

its cube.

594 = 15 + 29 + 34.

595 is a palindromic triangular number.

598 = 51 + 92 + 83.

607 is the exponent of a Mersenne prime.

610 is the 15th Fibonacci number.

614 is the smallest number that can be written as the sum of 3 squares

in 9 ways.

617 = 1!2 + 2!2 + 3!2 + 4!2.

619 is a strobogrammatic prime.

620 is the number of sided 7-hexes.

624 is the smallest number with the property that its first 5

multiples contain the digit 2.

625 is an automorphic number.

627 is the number of partitions of 20.

630 is the number of degree 13 irreducible polynomials over GF(2).

637 = 777 in base 9.

641 is the smallest prime factor of 225+1.

642 is the smallest number with the property that its first 6

multiples contain the digit 2.

645 is the largest n for which 1+2+3+...+n = 12+22+32+...+k2 for some

k.

646 is the number of connected planar graphs with 7 vertices.

650 is the sum of the first 12 squares.

651 is an nonagonal pentagonal number.

652 is the only known non-perfect number whose number of divisors and

sum of smaller divisors are perfect.

653 is the only known prime for which 5 is neither a primitive root or

a quadratic residue of 4n2+1.

660 is the order of a non-cyclic simple group.

666 is a palindromic triangular number.

670 is an octahedral number.

671 is a rhombic dodecahedral number.

672 is a multi-perfect number.

675 is the smallest order for which there are 17 groups.

676 is the smallest palindromic square number whose square root is not

palindromic.

679 is the smallest number with multiplicative persistence 5.

680 is the smallest tetrahedral number that is also the sum of 2

tetrahedral numbers.

682 = 11C6 + 11C8 + 11C2.

688 has a factorization using the same digits as itself.

689 is the smallest number that can be written as the sum of 3

distinct squares in 9 ways.

697 is a 12-hyperperfect number.

703 is a Kaprekar number.

704 is the number of sided octominoes.

707 is the smallest number whose reciprocal has period 12.

709 is the number of connected planar graphs with 9 edges.

710 is the number of connected graphs with 9 edges.

714 is the smallest number which has equal numbers of every digit in

bases 2 and 5.

715 = 13C4.

718 is the number of unlabeled topologies with 6 elements.

719 is the number of rooted trees with 10 vertices.

720 = 6!

721 is the smallest number which can be written as the difference of

two cubes in 2 ways.

724 is the number of different arrangements of 10 non-attacking queens

on an 10x10 chessboard.

726 is a pentagonal pyramidal number.

727 has the property that its square is the concatenation of two

consecutive numbers.

728 is the smallest number n where n and n+1 are both products of 5 or

more primes.

729 = 36.

730 is the number of connected bipartite graphs with 9 vertices.

731 is the number of planar partitions of 14.

732 = 17 + 26 + 35 + 44 + 53 + 62 + 71.

733 = 7 + 3! + (3!)!.

735 is the smallest number that is the concatenation of its distinct

prime factors.

736 = 7 + 36.

742 is the smallest number that is one more than triple its reverse.

743 is the number of independent sets of the graph of the

4-dimensional hypercube.

746 = 17 + 24 + 36.

750 is the Stirling number of the second kind S(10,8).

757 is the smallest number whose reciprocal has a period of 27.

762 is the first decimal digit of where a digit occurs four times in

a row.

764 is the number of 8x8 symmetric permutation matrices.

765 is a Kaprekar constant in base 2.

767 is the largest n so that n2 = mC0 + mC1 + mC2 + mC3 has a

solution.

777 is a repdigit in bases 6 and 10.

780 = (5+7)(5+8)(5+0).

781 = 11111 in base 5.

784 is the sum of the first 7 cubes.

786 is the largest known n for which 2nCn is not divisible by the

square of an odd prime.

787 is a palindromic prime.

791 is the smallest number n where either it or its neighbors are

divisible by the numbers from 1 to 12.

792 is the number of partitions of 21.

793 is one less than twice its reverse.

794 is the sum of the first 3 6th powers.

797 is the number of functional graphs on 9 vertices.

800 = 2222 in base 7.

802 is the number of isomers of C13H28.

810 is divisible by its reverse.

816 = 18C3.

819 is the smallest number so that it and its successor are both the

product of 2 primes and the square of a prime.

820 = 1111 in base 9.

822 is the number of planar graphs with 7 vertices.

835 is the 9th Motzkin number.

836 is a non-palindrome with a palindromic square.

840 is the smallest number divisble by 1 through 8.

841 is a square that is also the sum of 2 consecutive squares.

843 is the 14th Lucas number.

844 is the smallest number so that it and the next 4 numbers are all

squareful.

846 has the property that its square is the concatenation of two

consecutive numbers.

853 is the number of connected graphs with 7 vertices.

854 has the property that it and its square together use the digits

1-9 once.

855 is the smallest number which is the sum of 5 consecutive squares

or 2 consecutive cubes.

858 is the smallest palindrome with 4 different prime factors.

866 is the number of sided 10-iamonds.

870 is the sum of its digits and the cube of its digits.

872 is a value of n for which n!+1 is prime.

873 = 1! + 2! + 3! + 4! + 5! + 6!

877 is the 7th Bell number.

880 is the number of 4 x 4 magic squares.

888 has a cube that whose digits each occur 3 times.

889 is a Kaprekar constant in base 2.

891 is an octahedral number.

895 is a Woodall number.

899 is the product of twin primes.

900 is a square whose digits are non-increasing.

901 is the sum of the digits of the first 100 positive integers.

906 is the number of perfect graphs with 7 vertices.

907 is the largest n so that Q(n) has class number 3.

912 has exactly the same digits in 3 different bases.

913 has exactly the same digits in 3 different bases.

914 is the number of binary rooted trees with 15 vertices.

919 is a permutable prime.

924 is the 6th central binomial coefficient.

929 is a palindromic prime.

936 is a pentagonal pyramidal number.

941 is the smallest number which is the reverse of the sum of its

proper substrings.

945 is the smallest odd abundant number.

946 is a hexagonal pyramidal number.

951 is the number of functions from 8 unlabeled points to themselves.

952 = 93 + 53 + 23 + (9)(5)(2).

957 is a value of n for which sigma(n)=sigma(n+1).

960 is the sum of its digits and the cube of its digits.

961 is a square whose digits can be rotated to give another square.

966 is the Stirling number of the second kind S(8,3).

969 is a tetrahedral palindrome.

976 has a square formed by inserting a block of digits inside itself.

979 is the sum of the first 5 4th powers.

981 is the smallest number that has 5 different partitions into 3

parts with the same product.

986 = 19 + 28 + 36.

987 is the 16th Fibonacci number.

990 is a triangular number that is the product of 3 consecutive

integers.

991 is a permutable prime.

992 is the number of differential structures on the 11-dimensional

hypersphere.

993 is the smallest number with the property that its first 15

multiples contain the digit 9.

994 is the smallest number with the property that its first 18

multiples contain the digit 9.

995 has a square formed by inserting a block of digits inside itself.

996 has a square formed by inserting a block of digits inside itself.

997 is the smallest number with the property that its first 37

multiples contain the digit 9.

998 is the smallest number with the property that its first 55

multiples contain the digit 9.

999 is a Kaprekar number.

1000 = 103.

1001 is the smallest palindromic product of 3 consecutive primes.

1002 is the number of partitions of 22.

1005 is the smallest number whose English name contains all five

vowels exactly once.

1006 has a cube that is a concatenation of other cubes.

1016 is a stella octangula number.

1019 is a value of n for which one more than the product of the first

n primes is prime.

1021 is a value of n for which one more than the product of the first

n primes is prime.

1023 is the smallest number with 4 different digits.

1024 is the smallest number with 11 divisors.

1025 is the smallest number that can be written as the sum of a square

and a cube in 4 ways.

1029 is the smallest order for which there are 19 groups.

1031 is the length of the largest repunit that is known to be prime.

1033 = 81 + 80 + 83 + 83.

1036 = 4444 in base 6.

1044 is the number of graphs with 7 vertices.

1050 is the Stirling number of the second kind S(8,5).

1052 has the property that placing the last digit first gives 1 more

than twice it.

1056 is the area of the smallest non-square rectangle that can be

tiled with integer-sided squares.

1067 has exactly the same digits in 3 different bases.

1078 is the number of lattices on 9 unlabeled nodes.

1079 is the smallest number n where either it or its neighbors are

divisible by the numbers from 1 to 15.

1080 is the smallest number with 18 divisors.

1084 is the smallest number whose English name contains all five

vowels in order.

1089 is one ninth of its reverse.

1092 is the order of a non-cyclic simple group.

1093 is the smallest Wieferich prime.

1098 = 11 + 0 + 999 + 88.

1099 = 1 + 0 + 999 + 99.

1104 is a Keith number.

1105 is a rhombic dodecahedral number.

1106 is a truncated tetrahedral number.

1111 is a repdigit.

1116 is the number of polyaboloes with 8 half squares.

1122 = 33C1 + 33C1 + 33C2 + 33C2.

1124 is a number whose product of digits is equal to its sum of

digits.

1139 has the property that placing the last digit first gives 1 more

than 8 times it.

1140 is the smallest number whose divisors contain every digit at

least three times.

1141 is the smallest number whose 6th power can be written as the sum

of 7 6th powers.

1142 is a number whose product of digits is equal to its sum of

digits.

1148 is the number of ways to fold a strip of 9 stamps.

1153 is the smallest number with the property that its first 3

multiples contain the digit 3.

1155 is the product of 4 consecutive primes.

1156 is a square whose digits are non-decreasing.

1161 is the number of degree 14 irreducible polynomials over GF(2).

1166 is a heptagonal pyramidal number.

1167 is the smallest number whose 8th power can be written as the sum

of 9 8th powers.

1170 = 2222 in base 8.

1183 is the smallest number with the property that its first 4

multiples contain the digit 3.

1184 is an amicable number.

1185 = 11 + 1111 + 8 + 55.

1186 is the number of 11-iamonds.

1187 = 111 + 111 + 888 + 77.

1189 is the square root of a triangular number.

1193 and its reverse are prime, even if we append or prepend a 3 or 9.

1197 is the smallest number that contains as substrings the maximal

prime powers that divide it.

1200 = 3333 in base 7.

1206 has a factorization using the same digits as itself.

1207 is the product of two primes which are reverses of each other.

1210 is an amicable number.

1214 is a number whose product of digits is equal to its sum of

digits.

1215 is the smallest number n where n and n+1 are both products of 6

or more primes.

1222 is a hexagonal pyramidal number.

1224 is the smallest number that can be written as the sum of 4 cubes

in 3 ways.

1225 is a hexagonal square triangular number.

1229 is the number of primes less than 10000.

1230 has the property that 17 + 27 + 37 + 07 equals 1230 written in

base 8.

1231 has the property that 17 + 27 + 37 + 17 equals 1230 written in

base 8.

1233 = 122 + 332.

1241 is a centered cube number.

1243 is the number of essentially different ways to dissect a 18-gon

into 8 quadrilaterals.

1248 is the smallest number with the property that its first 6

multiples contain the digit 4.

1249 is the number of simplicial polyhedra with 11 vertices.

1255 is the number of partitions of 23.

1260 is the smallest number with 36 divisors.

1276 = 1111 + 22 + 77 + 66.

1278 = 1111 + 2 + 77 + 88.

1279 is the exponent of a Mersenne prime.

1285 is the number of 9-ominoes.

1287 = 13C5.

1294 is the number of 4 dimensional polytopes with 8 vertices.

1295 = 5555 in base 6.

1296 is the number of labeled trees with 6 vertices.

1300 is the sum of the first 4 5th powers.

1301 is the number of trees with 13 vertices.

1306 = 11 + 32 + 03 + 64.

1310 is the smallest number so that it and its neighbors are products

of three primes.

1320 = 12P3.

1330 = 21C3.

1331 is a cube containing only odd digits.

1334 is a value of n for which sigma(n)=sigma(n+1).

1364 is the 15th Lucas number.

1365 = 15C4.

1366 = 1 + 33 + 666 + 666.

1368 is the number of ways to fold a 3x3 rectangle of stamps.

1369 is a square whose digits are non-decreasing.

1370 = 12 + 372 + 02.

1371 = 12 + 372 + 12.

1376 is the smallest number with the property that it and its

neighbors are not cubefree.

1385 is the 8th Euler number.

1386 = 1 + 34 + 8 + 64.

1395 is a vampire number.

1405 is the sum of consecutive squares in 2 ways.

1412 is a number whose product of digits is equal to its sum of

digits.

1419 is a Zeisel number.

1421 is a number whose product of digits is equal to its sum of

digits.

1429 is the smallest number whose square has the first 3 digits the

same as the next 3 digits.

1430 is the 8th Catalan number.

1435 is a vampire number.

1444 is a square whose digits are non-decreasing.

1448 is the number of 8-hexes.

1449 is a stella octangula number.

1453 = 1111 + 4 + 5 + 333.

1454 = 11 + 444 + 555 + 444.

1455 is the number of subgroups of the symmetric group on 6 symbols.

1458 is the maximum determinant of a 11 x 11 matrix of 0's and 1's.

1459 = 11 + 444 + 5 + 999.

1467 has the property that e1467 is within 10-8 of an integer.

1469 is an octahedral number.

1470 is a pentagonal pyramidal number.

1476 is the number of graphs with 9 edges.

1477 is a value of n for which n!+1 is prime.

1494 is the sum of its proper divisors that contain the digit 4.

1500 = (5+1)(5+5)(5+0)(5+0).

1503 has a factorization using the same digits as itself.

1506 is the sum of its proper divisors that contain the digit 5.

1508 is a heptagonal pyramidal number.

1518 is the sum of its proper divisors that contain the digit 5.

1521 is the smallest number that can be written as the sum of 4

distinct cubes in 3 ways.

1530 is a vampire number.

1533 is a Kaprekar constant in base 2.

1537 has its largest proper divisor as a substring.

1540 is a tetrahedal triangular number.

1543 = 1111 + 55 + 44 + 333.

1547 is a hexagonal pyramidal number.

1555 is the largest n so that Q(n) has class number 4.

1562 = 22222 in base 5.

1563 is the smallest number with the property that its first 4

multiples contain the digit 6.

1575 is the number of partitions of 24.

1595 is the smallest quasi-Carmichael number in base 2.

1597 is the 17th Fibonacci number.

1600 = 4444 in base 7.

1606 is the number of strongly connected digraphs with 4 vertices.

1624 is the Stirling number of the first kind s(7,3).

1632 is the smallest number with the property that its first 5

multiples contain the digit 6.

1634 = 14 + 64 + 34 + 44.

1638 is a harmonic divisor number.

1639 is the number of binary rooted trees with 16 vertices.

1640 = 2222 in base 9.

1650 has exactly the same digits in 3 different bases.

1666 is the sum of the Roman numerals.

1676 = 11 + 62 + 73 + 64.

1680 is the smallest number with 40 divisors.

1681 is a square and each of its two 2-digit parts is square.

1688 is a truncated tetrahedral number.

1689 is the smallest composite number all of whose divisors (except 1)

contain the digit 9.

1695 is a rhombic dodecahedral number.

1701 is the Stirling number of the second kind S(8,4).

1705 is the smallest quasi-Carmichael number in base 4.

1715 = (1) (7)3 (1) (5).

1716 = 13C6.

1722 is a Giuga number.

1728 = 123.

1729 is the smallest number which can be written as the sum of 2 cubes

in 2 ways.

1730 is the sum of consecutive squares in 2 ways.

1734 is the sum of its proper divisors that contain the digit 8.

1755 = 3333 in base 8.

1763 is the product of twin primes.

1764 is the Stirling number of the first kind s(7,2).

1771 is a tetrahedral palindrome.

1782 is the smallest number n that is 3 times the sum of all the

2-digit numbers that can be made using the digits of n.

1785 is a Kaprekar constant in base 2.

1787 is the number of different arrangements (up to rotation and

reflection) of 12 non-attacking queens on a 12x12 chessboard.

1789 is the smallest number with the property that its first 4

multiples contain the digit 7.

1800 is a pentagonal pyramidal number.

1820 = 16C4.

1827 is a vampire number.

1828 is the 11th meandric number.

1834 is an octahedral number.

1842 is the number of rooted trees with 11 vertices.

1849 is the smallest composite number all of whose divisors (except 1)

contain the digit 4.

1854 is the number of derangements of 7 items.

1858 is the number of isomers of C14H30.

1873 is a value of n for which one less than the product of the first

n primes is prime.

1875 is the smallest order for which there are 21 groups.

1885 is a Zeisel number.

1890 is the smallest number whose divisors contain every digit at

least four times.

1900 is the largest palindrome in Roman numerals.

1905 is a Kaprekar constant in base 2.

1908 is the number of self-dual planar graphs with 22 edges.

1911 is a heptagonal pyramidal number.

1915 is the number of semigroups of order 5.

1925 is a hexagonal pyramidal number.

1947 is the number of planar partitions of 16.

1953 is a Kaprekar constant in base 2.

1958 is the number of partitions of 25.

1960 is the Stirling number of the first kind s(8,5).

1969 is the only known counterexample to a conjecture about modular

Ackermann functions.

1980 is the number of ways to fold a 2x4 rectangle of stamps.

1990 is a stella octangula number.

1998 is the largest number that is the sum of its digits and the cube

of its digits.

2000 = 5555 in base 7.

2002 = 14C5.

2008 is a Kaprekar constant in base 3.

2020 is a curious number.

2024 = 24C3.

2025 is a square that remains square if all its digits are

incremented.

2030 is the smallest number that can be written as a sum of 3 or 4

consecutive squares.

2038 is the number of Eulerian graphs with 9 vertices.

2041 is a 12-hyperperfect number.

2045 is the number of unlabeled partially ordered sets of 7 elements.

2047 is the smallest composite Mersenne number with prime exponent.

2048 is the smallest 11th power (besides 1).

2053 is a value of n for which one less than the product of the first

n primes is prime.

2073 is a Genocchi number.

2082 is the sum of its proper divisors that contain the digit 4.

2100 is divisible by its reverse.

2114 is a number whose product of digits is equal to its sum of

digits.

2132 is the maximum number of 11th powers needed to sum to any number.

2133 is a 2-hyperperfect number.

2141 is a number whose product of digits is equal to its sum of

digits.

2143 is the number of commutative semigroups of order 6.

2176 is the number of prime knots with 12 crossings.

2178 is the only number known which when multiplied by its reverse

yields a fourth power.

2182 is the number of degree 15 irreducible polynomials over GF(2).

2184 = 14P3.

2185 is the number of digits of 555.

2186 = 2222222 in base 3.

2187 = 37.

2188 is the 10th Motzkin number.

2197 = 133.

2201 is the only non-palindrome known to have a palindromic cube.

2203 is the exponent of a Mersenne prime.

2207 is the 16th Lucas number.

2208 is a Keith number.

2210 = 47C2 + 47C2 + 47C1 + 47C0.

2213 = 23 + 23 + 133.

2222 is the smallest number divisible by a 1-digit prime, a 2-digit

prime, and a 3-digit prime.

2223 is a Kaprekar number.

2255 is an octahedral number.

2261 = 2222 + 22 + 6 + 11.

2263 = 2222 + 2 + 6 + 33.

2272 has a cube that is a concatenation of other cubes.

2273 is the number of functional graphs on 10 vertices.

2274 is the sum of its proper divisors that contain the digit 7.

2275 is the sum of the first 6 4th powers.

2281 is the exponent of a Mersenne prime.

2285 is a non-palindrome with a palindromic square.

2295 is the number of self-dual binary codes of length 12.

2300 = 25C3.

2304 is the number of edges in a 9 dimensional hypercube.

2310 is the product of the first 5 primes.

2318 is the number of connected planar graphs with 10 edges.

2322 is the number of connected graphs with 10 edges.

2328 is the number of groups of order 128.

2331 is a centered cube number.

2336 is the number of sided 11-iamonds.

2340 = 4444 in base 8.

2343 = 33333 in base 5.

2354 = 2222 + 33 + 55 + 44.

2357 is the concatenation of the first 4 primes.

2359 = 2222 + 33 + 5 + 99.

2360 is a hexagonal pyramidal number.

2377 is a value of n for which one less than the product of the first

n primes is prime.

2380 = 17C4.

2400 = 6666 in base 7.

2401 is the 4th power of the sum of its digits.

2411 is a number whose product of digits is equal to its sum of

digits.

2427 = 21 + 42 + 23 + 74.

2431 is the product of 3 consecutive primes.

2436 is the number of partitions of 26.

2437 is the smallest number which is not prime when preceded or

followed by any digit 1-9.

2445 is a truncated tetrahedral number.

2448 is the order of a non-cyclic simple group.

2460 = 3333 in base 9.

2465 is a Carmichael number.

2499 is the number of connected planar Eulerian graphs with 10

vertices.

2500 is the number of sided 9-ominoes.

2511 is the smallest number so that it and its successor are both the

product of a prime and the 4th power of a prime.

2519 is the smallest number n where either n or n+1 is divisible by

the numbers from 1 to 12.

2520 is the smallest number divisible by 1 through 10.

2532 = 2222 + 55 + 33 + 222.

2538 has a square with 5/7 of the digits are the same.

2550 is a Kaprekar constant in base 4.

2571 is the smallest number with the property that its first 7

multiples contain the digit 1.

2576 has exactly the same digits in 3 different bases.

2580 is a Keith number.

2584 is the 18th Fibonacci number .

2592 = 25 92.

2600 = 26C3.

2601 is a pentagonal pyramidal number.

2606 is the number of polyhedra with 9 vertices.

2615 is the number of functions from 9 unlabeled points to themselves.

2620 is an amicable number.

2621 = 2222 + 66 + 222 + 111.

2623 = 2222 + 66 + 2 + 333.

2629 is the smallest number whose reciprocal has period 14.

2636 is a non-palindrome with a palindromic square.

2646 is the Stirling number of the second kind S(9,6).

2651 is a stella octangula number.

2657 is a value of n for which one more than the product of the first

n primes is prime.

2662 is a palindrome and the 2662nd triangular number is a palindrome.

2673 is the smallest number that can be written as the sum of 3 4th

powers in 2 ways.

2680 is the number of different arrangements of 11 non-attacking

queens on an 11x11 chessboard.

2683 is the largest n so that Q(n) has class number 5.

2685 is a value of n for which sigma(n)=sigma(n+1).

2697 and its product with 5 contain every digit from 1-9 exactly once.

2700 is the product of the first 5 triangular numbers.

2701 is the smallest number n which divides the average of the nth

prime and the primes surrounding it.

2728 is a Kaprekar number.

2730 = 15P3.

2736 is an octahedral number.

2737 = (2 * 7)3 - 7.

2744 = 143.

2745 divides the sum of the primes less than it.

2758 has the property that placing the last digit first gives 1 more

than triple it.

2780 = 18 + 27 + 36 + 45 + 54 + 63 + 72 + 81.

2801 = 11111 in base 7.

2802 is the sum of its proper divisors that contain the digit 4.

2805 is the smallest order of a cyclotomic polynomial whose

factorization contains 6 as a coefficient.

2821 is a Carmichael number.

2842 is the smallest number with the property that its first 4

multiples contain the digit 8.

2856 is a hexagonal pyramidal number.

2880 is the smallest number that can be written in the form

(a2-1)(b2-1) in 3 ways.

2890 is the smallest number in base 9 whose square contains the same

digits in the same proportion.

2916 is the product of the squares of a subset of its digits.

2920 is a heptagonal pyramidal number.

2922 is the sum of its proper divisors that contain the digit 4.

2924 is an amicable number.

2925 = 27C3.

2931 is the reverse of the sum of its proper substrings.

2938 is the number of binary rooted trees with 17 vertices.

2955 has a 5th power whose digits all occur twice.

2970 is a harmonic divisor number.

2974 is a value of n for which sigma(n)=sigma(n+1).

2996 = 2222 + 99 + 9 + 666.

2997 = 222 + 999 + 999 + 777.

2999 = 2 + 999 + 999 + 999.

3003 is the only number known to appear 8 times in Pascal's triangle.

3010 is the number of partitions of 27.

3012 is the sum of its proper divisors that contain the digit 5.

3024 = 9P4.

3025 is the sum of the first 10 cubes.

3036 is the sum of its proper divisors that contain the digit 5.

3059 is a centered cube number.

3060 = 18C4.

3068 is the number of 10-ominoes that tile the plane.

3069 is a Kaprekar constant in base 2.

3078 is a pentagonal pyramidal number.

3097 is the largest known number n with the property that in every

base, there exists a number that is n times the sum of its digits.

3103 = 22C3 + 22C1 + 22C0 + 22C3.

3106 is both the sum of the digits of the 16th and the 17th Mersenne

prime.

3110 = 22222 in base 6.

3120 is the product of the first 6 Fibonacci numbers.

3124 = 44444 in base 5.

3125 = 55.

3126 is a Sierpinski Number of the First Kind .

3135 is the smallest order of a cyclotomic polynomial whose

factorization contains 7 as a coefficient.

3136 is a square that remains square if all its digits are

decremented.

3137 is the number of planar partitions of 17.

3156 is the sum of its proper divisors that contain the digit 5.

3159 is the number of trees with 14 vertices.

3160 is the largest known n for which 2n!/(n!)2 does not contain a

prime factor less than 12.

3168 has a square whose reverse is also a square.

3174 is the sum of its proper divisors that contain the digit 5.

3187 and its product with 8 contain every digit from 1-9 exactly once.

3191 is the smallest number whose reciprocal has period 29.

3212 = 37 + 29 + 17 + 29.

3216 is the smallest number with the property that its first 6

multiples contain the digit 6.

3217 is the exponent of a Mersenne prime.

3229 is a value of n for which one more than the product of the first

n primes is prime.

3254 = 33 + 2222 + 555 + 444.

3259 = 33 + 2222 + 5 + 999.

3276 = 28C3.

3280 = 11111111 in base 3.

3281 is the sum of consecutive squares in 2 ways.

3282 is the sum of its proper divisors that contain the digit 4.

3301 is a value of n for which the nth Fibonacci number begins with

the digits in n.

3318 has exactly the same digits in 3 different bases.

3333 is a repdigit.

3334 is the number of 12-iamonds.

3340 = 3333 + 3 + 4 + 0.

3341 = 3333 + 3 + 4 + 1.

3342 = 3333 + 3 + 4 + 2.

3343 = 3333 + 3 + 4 + 3.

3344 = 3333 + 3 + 4 + 4.

3345 = 3333 + 3 + 4 + 5.

3346 = 3333 + 3 + 4 + 6.

3347 = 3333 + 3 + 4 + 7.

3348 = 3333 + 3 + 4 + 8.

3349 = 3333 + 3 + 4 + 9.

3360 = 16P3.

3367 is the smallest number which can be written as the difference of

2 cubes in 3 ways.

3369 is a Kaprekar constant in base 4.

3375 is a cube containing only odd digits.

3400 is a truncated tetrahedral number.

3413 = 11 + 22 + 33 + 44 + 55.

3417 is a hexagonal pyramidal number.

3420 is the order of a non-cyclic simple group.

3432 is the 7th central binomial coefficient.

3435 = 33 + 44 + 33 + 55.

3439 is a rhombic dodecahedral number.

3444 is a stella octangula number.

3465 is the smallest number with the property that its first 5

multiples contain the digit 3.

3468 = 682 - 342.

3492 is the number of labeled semigroups of order 4.

3510 = 6666 in base 8.

3511 is the largest known Wieferich prime.

3521 = 3333 + 55 + 22 + 111.

3522 is the sum of its proper divisors that contain the digit 7.

3527 is the number of ways to fold a strip of 10 stamps.

3536 is a heptagonal pyramidal number.

3541 is the smallest number whose reciprocal has period 20.

3571 is the 17th Lucas number.

3577 is a Kaprekar constant in base 2.

3599 is the product of twin primes.

3610 is a pentagonal pyramidal number.

3624 is the smallest number n where n through n+3 are all products of

4 or more primes.

3645 is the maximum determinant of a 12 x 12 matrix of 0's and 1's.

3654 = 29C3.

3655 is the sum of consecutive squares in 2 ways.

3684 is a Keith number.

3685 = (36 + 8) * 5.

3697 is the smallest number in base 6 whose square contains the same

digits in the same proportion.

3718 is the number of partitions of 28.

3740 is the sum of consecutive squares in 2 ways.

3743 is the number of polyaboloes with 9 half squares.

3763 is the largest n so that Q(n) has class number 6.

3784 has a factorization using the same digits as itself.

3786 = 34 + 74 + 8 + 64.

3792 occurs in the middle of its square.

3825 is a Kaprekar constant in base 2.

3836 is the maximum number of inversions in a permutation of length 7.

3840 = 10!!.

3864 = 3 * (-8 + 64).

3873 is a Kaprekar constant in base 4.

3876 = 19C4.

3882 is the sum of its proper divisors that contain the digit 4.

3894 is an octahedral number.

3906 = 111111 in base 5.

3911 and its reverse are prime, even if we append or prepend a 3 or 9.

3920 = (5+3)(5+9)(5+2)(5+0).

3925 is a centered cube number.

3926 is the 12th meandric number.

3937 is a Kaprekar constant in base 2.

3969 is a Kaprekar constant in base 2.

3972 = 3 + (9 * 7)2.

3977 has its largest proper divisor as a substring.

3985 = 3333 + 9 + 88 + 555.

4006 = 14C4 + 14C0 + 14C0 + 14C6.

4030 is an abundant number that is not the sum of some subset of its

divisors.

4032 is the number of connected bipartite graphs with 10 vertices.

4047 is a hexagonal pyramidal number.

4051 is the number of partitions of 6 items into ordered lists.

4060 = 30C3.

4062 is the smallest number with the property that its first 8

multiples contain the digit 2.

4080 = 17P3.

4093 is a value of n for which one less than the product of the first

n primes is prime.

4095 = 111111111111 in base 2.

4096 is the smallest number with 13 divisors.

4097 is the smallest number (besides 2) that can be written as the sum

of two cubes or the sum of two 4th powers.

4100 = 5555 in base 9.

4104 can be written as the sum of 2 cubes in 2 ways.

4112 is a number whose product of digits is equal to its sum of

digits.

4121 is a number whose product of digits is equal to its sum of

digits.

4128 is the smallest number with the property that its first 10

multiples contain the digit 2.

4140 is the 8th Bell number.

4150 = 45 + 15 + 55 + 05.

4151 = 45 + 15 + 55 + 15.

4152 = 45 + 15 + 55 + 2.

4153 = 45 + 15 + 55 + 3.

4154 = 45 + 15 + 55 + 4.

4155 = 45 + 15 + 55 + 5.

4156 = 45 + 15 + 55 + 6.

4157 = 45 + 15 + 55 + 7.

4158 = 45 + 15 + 55 + 8>.

4159 = 45 + 15 + 55 + 9.

4160 = 43 + 163 + 03.

4161 = 43 + 163 + 13.

4181 is the first composite number in the Fibonacci sequence with a

prime index.

4186 is a hexagonal, 13-gonal, triangular number.

4187 is the smallest Rabin-Miller pseudoprime with an odd reciprocal

period.

4199 is the product of 3 consecutive primes.

4200 is divisible by its reverse.

4207 is the number of cubic graphs with 16 vertices.

4211 is a number whose product of digits is equal to its sum of

digits.

4223 is the maximum number of 12th powers needed to sum to any number.

4224 is a palindrome that is one less than a square.

4231 is the number of labeled partially ordered sets with 5 elements.

4233 is a heptagonal pyramidal number.

4243 = 444 + 22 + 444 + 3333.

4253 is the exponent of a Mersenne prime.

4293 has exactly the same digits in 3 different bases.

4297 is a value of n for which one less than the product of the first

n primes is prime.

4305 has exactly the same digits in 3 different bases.

4310 has exactly the same digits in 3 different bases.

4320 = (6+4)(6+3)(6+2)(6+0).

4332 = 444 + 3333 + 333 + 222.

4335 = 444 + 3333 + 3 + 555.

4336 = 4 + 3333 + 333 + 666.

4339 = 4 + 3333 + 3 + 999.

4347 is a heptagonal pentagonal number.

4356 is two thirds of its reversal.

4357 is the smallest number with the property that its first 5

multiples contain the digit 7.

4364 is a value of n for which sigma(n)=sigma(n+1).

4368 = 16C5.

4381 is a stella octangula number.

4396 = (157)(28) and each digit is contained in the equation exactly

once.

4409 is prime, but changing any digit makes it composite.

4423 is the exponent of a Mersenne prime.

4425 is the sum of the first 5 5th powers.

4434 is the sum of its proper divisors that contain the digit 7.

4444 is a repdigit.

4489 is a square whose digits are non-decreasing.

4495 = 31C3.

4505 is a Zeisel number.

4503 is the largest number that is not the sum of 4 or fewer squares

of composites.

4506 is the sum of its proper divisors that contain the digit 5.

4510 = 4444 + 55 + 11 + 0.

4511 = 4444 + 55 + 11 + 1.

4512 = 4444 + 55 + 11 + 2.

4513 = 4444 + 55 + 11 + 3.

4514 = 4444 + 55 + 11 + 4.

4515 = 4444 + 55 + 11 + 5.

4516 = 4444 + 55 + 11 + 6.

4517 = 4444 + 55 + 11 + 7.

4518 = 4444 + 55 + 11 + 8.

4519 = 4444 + 55 + 11 + 9.

4523 has a square in base 2 that is palindromic.

4535 is the number of unlabeled topologies with 7 elements.

4536 is the Stirling number of the first kind s(9,6).

4547 is a value of n for which one more than the product of the first

n primes is prime.

4548 is the sum of its proper divisors that contain the digit 7.

4565 is the number of partitions of 29.

4576 is a truncated tetrahedral number.

4579 is an octahedral number.

4583 is a value of n for which one less than the product of the first

n primes is prime.

4607 is a Woodall number.

4609 = 4444 + 66 + 0 + 99.

4613 is the number of graphs with 10 edges.

4620 is the largest order of a permutation of 30 or 31 elements.

4624 = 44 + 46 + 42 + 44.

4641 is a rhombic dodecahedral number.

4655 is the number of 10-ominoes.

4665 = 33333 in base 6.

4676 is the sum of the first 7 4th powers.

4681 = 11111 in base 8.

4683 is the number of orderings of 6 objects with ties allowed.

4705 is the sum of consecutive squares in 2 ways.

4713 is a Cullen number.

4734 is the sum of its proper divisors that contain the digit 7.

4750 is a hexagonal pyramidal number.

4752 = (4+4)(4+7)(4+5)(4+2).

4760 is the sum of consecutive squares in 2 ways.

4766 is the number of rooted trees with 12 vertices.

4787 is a value of n for which one more than the product of the first

n primes is prime.

4788 is a Keith number.

4793 = 4444 + 7 + 9 + 333.

4807 is the smallest quasi-Carmichael number in base 10.

4845 = 20C4.

4851 is a pentagonal pyramidal number.

4862 is the 9th Catalan number.

4863 is the smallest number that cannot be written as the sum of 273

8th powers.

4890 is the sum of the first 4 6th powers.

4896 = 18P3.

4900 is the only number which is both square and square pyramidal

(besides 1).

4913 is the cube of the sum of its digits.

4920 = 6666 in base 9.

4941 is a centered cube number.

4960 = 32C3.

4974 is the sum of its proper divisors that contain the digit 8.

5000 is the largest number whose English name does not repeat any

letters.

5005 is the smallest palindromic product of 4 consecutive primes.

5016 is a heptagonal pyramidal number.

5020 is an amicable number.

5039 is the number of planar partitions of 18.

5040 = 7!

5041 is the largest square known of the form n!+1.

5050 is the sum of the first 100 integers.

5054 = 555 + 0 + 55 + 4444.

5055 has exactly the same digits in 3 different bases.

5100 is divisible by its reverse.

5104 is the smallest number that can be written as the sum of 3 cubes

in 3 ways.

5120 is the number of edges in a 10 dimensional hypercube.

5141 is the only four digit number that is reversed in hexadecimal.

5142 is the sum of its proper divisors that contain the digit 7.

5143 = 555 + 111 + 4444 + 33.

5160 = 5! + (1+6)! + 0.

5161 = 5! + (1+6)! + 1!.

5162 = 5! + (1+6)! + 2.

5163 = 5! + (1+6)! + 3.

5164 = 5! + (1+6)! + 4.

5165 = 5! + (1+6)! + 5.

5166 = 5! + (1+6)! + 6.

5167 = 5! + (1+6)! + 7.

5168 = 5! + (1+6)! + 8.

5169 = 5! + (1+6)! + 9.

5183 is the product of twin primes.

5187 is the only number n known for which phi(n-1) = phi(n) =

phi(n+1).

5200 is divisible by its reverse.

5244 is the sum of consecutive squares in 2 ways.

5269 is the number of binary rooted trees with 18 vertices.

5274 is the sum of its proper divisors that contain the digit 7.

5332 is a Kaprekar constant in base 3.

5340 is an octahedral number.

5346 = (198)(27) and each digit is contained in the equation exactly

once.

5400 is divisible by its reverse.

5434 is the sum of consecutive squares in 2 ways.

5456 and its reverse are tetrahedral numbers.

5460 is the largest order of a permutation of 32 or 33 elements.

5474 is a stella octangula number.

5477 and its reverse are both one more than a square.

5525 is the smallest number that can be written as the sum of 2

squares in 6 ways.

5530 is a hexagonal pyramidal number.

5555 is a repdigit.

5564 is an amicable number.

5566 is a pentagonal pyramidal number.

5600 is a Kaprekar constant in base 6.

5602 = 22222 in base 7.

5604 is the number of partitions of 30.

5610 is divisible by its reverse.

5616 is the order of a non-cyclic simple group.

5682 is the sum of its proper divisors that contain the digit 4.

5693 = 5555 + 6 + 99 + 33.

5696 = 5555 + 66 + 9 + 66.

5700 is divisible by its reverse.

5719 is a Zeisel number.

5723 has the property that its square starts with its reverse.

5740 = 7777 in base 9.

5775 is the product of two different substrings of its digits.

5776 is the square of the last half of its digits.

5777 is the smallest number (besides 1) which is not the sum of a

prime and twice a square.

5778 is the largest Lucas number which is also a triangular number.

5784 = 555 + 777 + 8 + 4444.

5786 = 5555 + 77 + 88 + 66.

5795 is a Cullen number.

5796 = (138)(42) and each digit is contained in the equation exactly

once.

5798 is the 11th Motzkin number.

5814 = 19P3.

5823 and its triple contain every digit from 1-9 exactly once.

5830 is an abundant number that is not the sum of some subset of its

divisors.

5832 is the cube of the sum of its digits.

5851 is the only prime so that it, its square, and its cube all have

the same sum of digits.

5872 = 5555 + 88 + 7 + 222.

5880 is the Stirling number of the second kind S(10,7).

5890 is a heptagonal pyramidal number.

5906 is the smallest number which is the sum of 2 rational 4th powers

but is not the sum of two integer 4th powers.

5913 = 1! + 2! + 3! + 4! + 5! + 6! + 7!

5915 is the sum of consecutive squares in 2 ways.

5923 is the largest n so that Q(n) has class number 7.

5929 is a square which is also the sum of 11 consecutive squares.

5940 is divisible by its reverse.

5963 = 5555 + 9 + 66 + 333.

5972 is the smallest number that appears in its factorial 8 times.

5974 is the number of connected planar graphs with 8 vertices.

5984 = 34C3.

5985 = 21C4.

5986 and its prime factors contain every digit from 1-9 exactly once.

5993 is the largest number known which is not the sum of a prime and

twice a square.

5994 is the number of lattices on 10 unlabeled nodes.

5995 is a palindromic triangular number.

5996 is a truncated tetrahedral number.

6001 has a cube that is a concatenation of other cubes.

6006 is the smallest palindrome with 5 different prime factors.

6008 = 14C6 + 14C0 + 14C0 + 14C8.

6020 is the number of Hamiltonian graphs with 8 vertices.

6048 is the order of a non-cyclic simple group.

6072 is the order of a non-cyclic simple group.

6084 is the sum of the first 12 cubes.

6095 is a rhombic dodecahedral number.

6102 is the largest number n known where phi(n) is the the reverse of

n.

6119 is a centered cube number.

6141 is a Kaprekar constant in base 2.

6144 = (6) (1) (4) (4)4.

6174 is the Kaprekar constant for 4-digit numbers.

6176 is the last 4-digit sequence to appear in the decimal expansion

of .

6181 is an octahedral number.

6188 = 17C5.

6200 is a harmonic divisor number.

6220 = 44444 in base 6.

6221 = 666 + 2222 + 2222 + 1111.

6223 = 666 + 2222 + 2 + 3333.

6225 = 666 + 2 + 2 + 5555.

6232 is an amicable number.

6248 is the smallest number with the property that its first 8

multiples contain the digit 4.

6249 is the smallest number with the property that its first 10

multiples contain the digit 4.

6257 is the number of essentially different ways to dissect a 20-gon

into 9 quadrilaterals.

6300 is divisible by its reverse.

6307 is the largest n so that Q(n) has class number 8.

6312 is the sum of its proper divisors that contain the digit 5.

6348 is a pentagonal pyramidal number.

6368 is an amicable number.

6380 is a value of n for which n!+1 is prime.

6389 is the number of functional graphs on 11 vertices.

6391 is a hexagonal pyramidal number.

6400 is a square whose digits are non-increasing.

6435 = 15C7.

6455 = (64 - 5) * 5.

6489 is half again as large as the sum of its proper divisors.

6500 is a number n whose sum of the factorials of its digits is equal

to pi(n).

6501 has a square whose reverse is also a square.

6510 is a number n whose sum of the factorials of its digits is equal

to pi(n).

6511 is a number n whose sum of the factorials of its digits is equal

to pi(n).

6521 is a number n whose sum of the factorials of its digits is equal

to pi(n).

6524 has the property that its square starts with its reverse.

6545 and its reverse are tetrahedral numbers.

6556 is the largest palindrome that can be made using 5 digits and the

4 arithmetic operations.

6560 is the smallest number n where n and n+1 are both products of 7

or more primes.

6561 = 38.

6569 is a value of n for which one less than the product of the first

n primes is prime.

6572 is the number of 9-hexes.

6578 is the smallest number which can be written as the sum of 3 4th

powers in 2 ways.

6588 is the number of sided 12-iamonds.

6593 = 6 + 5555 + 999 + 33.

6601 is a Carmichael number.

6611 is a Cullen number.

6620 is the number of 11-ominoes that tile the plane.

6636 has exactly the same digits in 3 different bases.

6643 is the smallest number which is palindromic in bases 2 and 3.

6666 is a repdigit.

6667 is the number of self-dual planar graphs with 24 edges.

6680 = 6666 + 6 + 8 + 0.

6681 = 6666 + 6 + 8 + 1.

6682 = 6666 + 6 + 8 + 2.

6683 = 6666 + 6 + 8 + 3.

6684 = 6666 + 6 + 8 + 4.

6685 = 6666 + 6 + 8 + 5.

6686 = 6666 + 6 + 8 + 6.

6687 = 6666 + 6 + 8 + 7.

6688 = 6666 + 6 + 8 + 8.

6689 = 6666 + 6 + 8 + 9.

6720 = 8P5.

6729 and its double together use each of the digits 1-9 exactly once.

6735 is a stella octangula number.

6765 is the 20th Fibonacci number.

6769 is the Stirling number of the first kind s(8,4).

6772 = 6666 + 7 + 77 + 22.

6779 = 6666 + 7 + 7 + 99.

6788 is the smallest number with multiplicative persistence 6.

6840 = 20P3.

6842 is the number of partitions of 31.

6859 = 193.

6860 is a heptagonal pyramidal number.

6864 = 6666 + 88 + 66 + 44.

6880 is a vampire number.

6888 has a square with 3/4 of the digits are the same.

6889 is a strobogrammatic square.

6912 = (6) (9) (1) (2)7.

6922 is the number of polycubes containing 8 cubes.

6930 is the square root of a triangular number.

6940 is the sum of its proper divisors that contain the digit 3.

6942 is the number of labeled topologies with 5 elements.

6951 has exactly the same digits in 3 different bases.

6952 = (1738)(4) and each digit is contained in the equation exactly

once.

6953 = 66 + 999 + 5555 + 333.

6966 is the number of planar graphs with 8 vertices.

7106 is an octahedral number.

7140 is the largest number which is both triangular and tetrahedral.

7161 is a Kaprekar constant in base 2.

7192 is an abundant number that is not the sum of some subset of its

divisors.

7200 is a pentagonal pyramidal number.

7230 is the sum of consecutive squares in 2 ways.

7254 = (186)(39) and each digit is contained in the equation exactly

once.

7272 is a Kaprekar number.

7314 is the smallest number so that it and its successor are both

products of 4 primes.

7315 = 22C4.

7318 is the number of functions from 10 unlabeled points to

themselves.

7337 is a hexagonal pyramidal number.

7381 = 11111 in base 9.

7385 is a Keith number.

7422 is the sum of its proper divisors that contain the digit 7.

7429 is the product of 3 consecutive primes.

7436 is the number of 6x6 alternating sign matrices.

7471 is a centered cube number.

7494 is the sum of its proper divisors that contain the digit 4.

7496 = 777 + 44 + 9 + 6666.

7512 is the sum of its proper divisors that contain the digit 5.

7549 is the largest known prime p where no numbers of the form p-n2

are prime.

7560 is the smallest number with 64 divisors.

7574 is the sum of consecutive squares in 2 ways.

7581 is the number of monotone Boolean functions of 5 variables.

7586 = 777 + 55 + 88 + 6666.

7595 is the number of simplicial polyhedra with 12 vertices.

7647 is a Keith number.

7663 is the product of two primes which are reverses of each other.

7665 is a Kaprekar constant in base 2.

7672 = 777 + 6666 + 7 + 222.

7673 is the smallest number with the property that its first 8

multiples contain the digit 3.

7679 = 7 + 6666 + 7 + 999.

7683 is a truncated tetrahedral number.

7693 is a value of n for which the sum of the first n primes is a

palindrome.

7710 is the number of degree 17 irreducible polynomials over GF(2).

7734 is the sum of its proper divisors that contain the digit 8.

7741 is the number of trees with 15 vertices.

7744 is the only square known with no isolated digits.

7745 and its reverse are both one more than a square.

7770 = 37C3.

7775 = 55555 in base 6.

7776 is a 5th power whose digits are non-increasing.

7777 is a Kaprekar number.

7800 is the order of a non-cyclic simple group.

7810 has the property that its square is the concatenation of two

consecutive numbers.

7812 = 222222 in base 5.

7825 is a rhombic dodecahedral number.

7851 = 7777 + 8 + 55 + 11.

7852 = (1963)(4) and each digit is contained in the equation exactly

once.

7856 = 7777 + 8 + 5 + 66.

7905 is a Kaprekar constant in base 2.

7909 is a Keith number.

7920 is the order of the smallest sporadic group.

7931 is a heptagonal pyramidal number.

7936 is the 9th Euler number.

7941 = 7777 + 9 + 44 + 111.

7942 = 7777 + 99 + 44 + 22.

7946 = 7777 + 99 + 4 + 66.

7980 is the smallest number whose divisors contain every digit at

least 7 times.

7993 is one less than twice its reverse.

8000 is the smallest cube which is also the sum of 4 consecutive

cubes.

8001 is a Kaprekar constant in base 2.

8008 = 16C6.

8026 is the number of planar partitions of 19.

8042 is the largest number known which cannot be written as a sum of 7

or fewer cubes.

8071 is the number of connected graphs with 11 edges.

8100 is divisible by its reverse.

8119 is an octahedral number.

8125 is the smallest number that can be written as the sum of 2

squares in 5 ways.

8128 is the 4th perfect number.

8176 is a stella octangula number.

8184 has exactly the same digits in 3 different bases.

8190 is a harmonic divisor number.

8191 is a Mersenne prime.

8192 is the smallest 13th power (besides 1).

8200 = 8 + 213 + 0 + 0.

8201 = 8 + 213 + 0 + 1.

8202 = 8 + 213 + 0 + 2.

8203 = 8 + 213 + 0 + 3.

8204 = 8 + 213 + 0 + 4.

8205 = 8 + 213 + 0 + 5.

8206 = 8 + 213 + 0 + 6.

8207 = 8 + 213 + 0 + 7.

8208 = 84 + 24 + 04 + 84.

8209 = 8 + 213 + 0 + 9.

8226 is the sum of its proper divisors that contain the digit 4.

8281 is the only 4-digit square whose two 2-digit pairs are

consecutive.

8349 is the number of partitions of 32.

8372 is a hexagonal pyramidal number.

8375 is the smallest number which has equal numbers of every digit in

bases 2 and 6.

8384 is the maximum number of 13th powers needed to sum to any number.

8400 is divisible by its reverse.

8403 = 33333 in base 7.

8415 is the smallest number which has equal numbers of every digit in

bases 3 and 6.

8436 = 38C3.

8486 = 888 + 44 + 888 + 6666.

8510 is a value of n for which the sum of the first n primes is a

palindrome.

8538 is the sum of its proper divisors that contain the digit 4.

8562 is the sum of its proper divisors that contain the digit 4.

8568 = 18C5.

8586 has exactly the same digits in 3 different bases.

8614 and its prime factors contain every digit from 1-9 exactly once.

8664 = 888 + 6666 + 666 + 444.

8682 is the sum of its proper divisors that contain the digit 4.

8712 is 4 times its reverse.

8732 has exactly the same digits in 3 different bases.

8736 is the smallest number that appears in its factorial 10 times.

8753 = 88 + 7777 + 555 + 333.

8758 = 88 + 7777 + 5 + 888.

8763 and its successor have the same digits in their prime

factorization.

8772 is the sum of the first 8 4th powers.

8778 is a palindromic triangular number.

8826 is the sum of its proper divisors that contain the digit 4.

8833 = 882 + 332.

8855 = 23C4.

8888 is a repdigit.

8910 is divisible by its reverse.

8911 is a Carmichael number.

8922 is the sum of its proper divisors that contain the digit 4.

8930 = 8888 + 9 + 33 + 0.

8931 = 8888 + 9 + 33 + 1.

8932 = 8888 + 9 + 33 + 2.

8933 = 8888 + 9 + 33 + 3.

8934 = 8888 + 9 + 33 + 4.

8935 = 8888 + 9 + 33 + 5.

8936 = 8888 + 9 + 33 + 6.

8937 = 8888 + 9 + 33 + 7.

8938 = 8888 + 9 + 33 + 8.

8939 = 8888 + 9 + 33 + 9.

8964 is the smallest number with the property that its first 6

multiples contain the digit 8.

8970 = 8 + 94 + 74 + 0.

8971 = 8 + 94 + 74 + 1.

8972 = 8 + 94 + 74 + 2.

8973 = 8 + 94 + 74 + 3.

8974 = 8 + 94 + 74 + 4.

8975 = 8 + 94 + 74 + 5.

8976 = 8 + 94 + 74 + 6.

8977 = 8 + 94 + 74 + 7.

8978 = 8 + 94 + 74 + 8.

8979 = 8 + 94 + 74 + 9.

8991 is the smallest number so that it and its successor are both the

product of a prime and the 5th power of a prime.

9009 is a centered cube number.

9012 is the sum of its proper divisors that contain the digit 5.

9091 is the only prime known whose reciprocal has period 10.

9108 is a heptagonal pyramidal number.

9126 is a pentagonal pyramidal number.

9139 = 39C3.

9174 is the sum of its proper divisors that contain the digit 5.

9189 is the number of sided 10-ominoes.

9224 is an octahedral number.

9233 is the number of different arrangements (up to rotation and

reflection) of 13 non-attacking queens on a 13x13 chessboard.

9240 = 22P3.

9253 is the smallest number that appears in its factorial 9 times.

9261 = 213.

9272 is an abundant number that is not the sum of some subset of its

divisors.

9330 is the Stirling number of the second kind S(10,3).

9331 = 111111 in base 6.

9349 is the 19th Lucas number.

9362 = 22222 in base 8.

9376 is an automorphic number.

9385 is the sum of consecutive squares in 2 ways.

9386 = 99 + 333 + 8888 + 66.

9408 is the number of reduced 6 x 6 Latin squares.

9451 is the number of binary rooted trees with 19 vertices.

9468 is the sum of its proper divisorsproper divisors that contain the

digit 7.

9474 = 94 + 44 + 74 + 44.

9477 is the maximum determinant of a 13 x 13 matrix of 0's and 1's.

9496 is the number of 10x10 symmetric permutation matrices.

9500 is a hexagonal pyramidal number.

9563 = 9 + 5555 + 666 + 3333.

9568 = 9 + 5 + 666 + 8888.

9608 is the number of digraphs with 5 vertices.

9625 has a square formed by inserting a block of digits inside itself.

9653 = 99 + 666 + 5555 + 3333.

9658 = 99 + 666 + 5 + 8888.

9660 is a truncated tetrahedral number.

9689 is the exponent of a Mersenne prime.

9726 is the smallest number in base 5 whose square contains the same

digits in the same proportion.

9784 is the number of 2 state Turing machines which halt.

9789 is the smallest number that appears in its factorial 11 times.

9801 is 9 times its reverse.

9809 is a stella octangula number.

9828 is the order of a non-cyclic simple group.

9841 = 111111111 in base 3.

9855 is a rhombic dodecahedral number.

9862 is the number of knight's tours on a 6 x 6 chess board.

9876 is the largest 4-digit number with different digits.

9880 = 40C3.

9901 is the only prime known whose reciprocal has period 12.

9941 is the exponent of a Mersenne prime.

9976 has a square formed by inserting a block of digits inside itself.

9988 is the number of prime knots with 13 crossings.

9995 has a square formed by inserting a block of digits inside itself.

9996 has a square formed by inserting a block of digits inside itself.

9999 is a Kaprekar number.

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