divisors-делители
algebra-алгебра primes-простые числа

sums of powers-суммы степеней
powers/polygonal-степени/многоугольники
matrices-матрицы graphs-графы
combinatorics-комбинаторика
Fibonacci-числа Фибоначчи
digits-цифры perfect/amicable-совершенные/дружественные
bases-основание счисления
repdigits-повторяющиеся
цифры geometry-геометрия

2002 = _{14}C_{5}.

2008 is a Karmekar number in base 3.

2020 is a curious number.

2024 = _{24}C_{3}.

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 11^{th} power (besides
1).

2053 is the largest known value of n for which the
product of the first n primes - 1 is prime.

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

2100 is divisible by its reverse.

2133 is a 2-hyperperfect number.

2143 is the number of commutative semigroups of order
6.

2176 = 222 + 1111 + 777 + 66.

2178 is one fourth of its reverse.

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

2184 = _{14}P_{3}.

2186 = 2222222 in base 3.

2187 = 3^{7}.

2188 is the 10^{th} Motzkin number.

2197 = 13^{3}.

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

2203 is the exponent of a Mersenne prime.

2207 is the 16^{th} Lucas number.

2210 = _{47}C_{2} + _{47}C_{2}
+ _{47}C_{1} + _{47}C_{0}.

2213 = 2^{3} + 2^{3} + 13^{3}.

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.

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 digraphs on 10
vertices.

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

2275 is the sum of the first 6 4^{th}
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 = _{25}C_{3}.

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.

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.

2380 = _{17}C_{4}.

2400 = 6666 in base 7.

2401 is the 4^{th} power of the sum of its
digits.

2427 = 2^{1} + 4^{2} + 2^{3}
+ 7^{4}.

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.

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.

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 Karmekar number 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.

2584 is the 18^{th} Fibonacci number.

2592 = 2^{5} 9^{2}.

2600 = _{26}C_{3}.

2606 is the number of polyhedra with 9 vertices.

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

2620 is amicable.

2621 = 2222 + 66 + 222 + 111.

2623 = 2222 + 66 + 2 + 333.

2636 is a non-palindrome with a palindromic square.

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

2657 is the largest known value of n for which the
product of the first n primes + 1 is prime.

2673 is the smallest number that can be written as
the sum of 3 4^{th} powers in 2 ways.

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

2700 is the product of the first 5 triangular
numbers.

2728 is a Kaprekar number.

2730 = _{15}P_{3}.

2744 = 15^{3}.

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 = 1^{8} + 2^{7} + 3^{6}
+ 4^{5} + 5^{4} + 6^{3} + 7^{2} + 8^{1}.

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
containing 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.

2880 is the smallest number that can be written in
the form (a^{2}-1)(b^{2}-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.

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

2924 is amicable.

2925 = _{27}C_{3}.

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 5^{th} power whose digits all
occur twice.

2970 is a harmonic divisor number.

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 = _{9}P_{4}.

3025 is the sum of the first 10 cubes.

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

3060 = _{18}C_{4}.

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

3069 is a Karmekar number in base 2.

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 = _{22}C_{3} + _{22}C_{1}
+ _{22}C_{0} + _{22}C_{3}.

3110 = 22222 in base 6.

3120 is the product of the first 6 Fibonacci numbers.

3124 = 44444 in base 5.

3125 = 5^{5}.

3135 is the smallest order of a cyclotomic polynomial
containing 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.

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.

3254 = 33 + 2222 + 555 + 444.

3259 = 33 + 2222 + 5 + 999.

3276 = _{28}C_{3}.

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.

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 = _{16}P_{3}.

3367 is the smallest number which can be written as
the difference of 2 cubes in 3 ways.

3369 is a Karmekar number in base 4.

3375 is a cube containing only odd digits.

3413 = 1^{1} + 2^{2} + 3^{3}
+ 4^{4} + 5^{5}.

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

3432 is the 7^{th} central binomial
coefficient.

3435 = 3^{3} + 4^{4} + 3^{3}
+ 5^{5}.

3465 is the smallest number with the property that
its first 5 multiples contain the digit 3.

3468 = 68^{2} - 34^{2}.

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 10 stamps.

3571 is the 17^{th} Lucas number.

3577 is a Karmekar number in base 2.

3599 is the product of twin primes.

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 = _{29}C_{3}.

3655 is the sum of consecutive squares in 2 ways.

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 polyabloes with 9 half squares.

3784 has a factorization using the same digits as
itself.

3792 occurs in the middle of its square.

3825 is a Karmekar number in base 2.

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

3840 = 10!!.

3873 is a Karmekar number in base 4.

3876 = _{19}C_{4}.

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

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).

3926 is the 12^{th} meandric number.

3937 is a Karmekar number in base 2.

3969 is a Karmekar number in base 2.

3977 has its largest proper divisor as a substring.

3985 = 3333 + 9 + 88 + 555.

4006 = _{14}C_{4} + _{14}C_{0}
+ _{14}C_{0} + _{14}C_{6}.

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.

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

4060 = _{30}C_{3}.

4062 is the smallest number with the property that
its first 8 multiples contain the digit 2.

4080 = _{17}P_{3}.

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 fourth powers.

4100 = 5555 in base 9.

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

4128 is the smallest number with the property that
its first 10 multiples contain the digit 2.

4140 is the 8^{th} Bell number.

4150 = 4^{5} + 1^{5} + 5^{5}
+ 0^{5}.

4151 = 4^{5} + 1^{5} + 5^{5}
+ 1^{5}.

4160 = 4^{3} + 16^{3} + 0^{3}.

4161 = 4^{3} + 16^{3} + 1^{3}.

4181 is the first composite number in the Fibonacci
sequence with a prime index.

4186 is triangular, hexagonal, and 13-gonal.

4199 is the product of 3 consecutive primes.

4200 is divisible by its reverse.

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

4231 is the number of labeled posets with 5
elements.

4243 = 444 + 22 + 444 + 3333.

4253 is the exponent of a Mersenne prime.

4293 has exactly the same digits in 3 different
bases.

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 an 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.

4368 = _{16}C_{5}.

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 5^{th}
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 = _{31}C_{3}.

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.

4535 is the number of unlabeled topologies with 7
elements.

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

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

4565 is the number of partitions of 29.

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 = 4^{4} + 4^{6} + 4^{2}
+ 4^{4}.

4655 is the number of 10-ominoes.

4665 = 33333 in base 6.

4676 is the sum of the first 7 4^{th}
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.

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.

4793 = 4444 + 7 + 9 + 333.

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

4845 = _{20}C_{4}.

4862 is the 9^{th} Catalan number.

4863 is the smallest number that cannot be written
as the sum of 273 8^{th} powers.

4890 is the sum of the first 4 6^{th}
powers.

4896 = _{18}P_{3}.

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.

4960 = _{32}C_{3}.

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

5005 is the smallest palindromic product of 4
consecutive primes.

5020 is amicable.

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.

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 known which is coprime to
the same number of smaller integers as its neighbors.

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 Karmekar number in base 3.

5400 is divisible by its reverse.

5434 is the sum of consecutive squares in 2 ways.

5456 and its reverse are tetrahedral.

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

5525 is the smallest number that can be written as
the sum of 2 squares in 6 ways.

5555 is a repdigit.

5564 is amicable.

5600 is a Karmekar number 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.

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

5740 = 7777 in base 9.

5775 is a plaindrome that is one less than a
square.

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.

5798 is the 11^{th} Motzkin number.

5814 = _{19}P_{3}.

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.

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

5940 is divisible by its reverse.

5872 = 5555 + 88 + 7 + 222.

5906 is the smallest number which is the sum of 2
rational 4^{th} powers but is not the sum of two integer 4^{th} powers.

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

5915 is the sum of consecutive squares in 2 ways.

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

5963 = 5555 + 9 + 66 + 333.

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

5984 = _{34}C_{3}.

5985 = _{21}C_{4}.

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.

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

6006 is the smallest palindrome with 5 different
prime factors.

6008 = _{14}C_{6} + _{14}C_{0}
+ _{14}C_{0} + _{14}C_{8}.

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.

6102 is the largest number n known where the number
of numbers smaller than n and relatively prime to n is the th reverse of n.

6141 is a Karmekar number 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 pi.

6188 = _{17}C_{5}.

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 amicable.

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.

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

6368 is amicable.

6380 is the largest known value of n for which
n!+1 is prime.

6389 is the number of functional digraphs on 11
vertices.

6400 is a square whose digits are non-increasing.

6435 = _{15}C_{7}.

6501 has a square whose reverse is also a square.

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

6545 and its reverse are tetrahedral.

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 = 3^{8}.

6572 is the number of 9-hexes.

6578 is the smallest number which can be written as
the sum of 3 4^{th} 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 = _{8}P_{5}.

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

6765 is the 20^{th} 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 = _{20}P_{3}.

6842 is the number of partitions of 31.

6859 = 19^{3}.

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.

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 = 6666 + 9 + 55 + 222.

6953 = 66 + 999 + 5555 + 333.

6966 is the number of planar graphs with 8
vertices.

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

7161 is a Karmekar number in base 2.

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

7230 is the sum of consecutive squares in 2 ways.

7272 is a Kaprekar number.

7314 is the smallest number so that it and its
successor are products of 4 primes.

7315 = _{22}C_{4}.

7318 is the number of functions from 10 unlabeled
points to themselves.

7381 = 11111 in base 9.

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 alternating sign 6x6 matrices.

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-n^{2} 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.

7665 is a Karmekar number 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.

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.

7770 = _{37}C_{3}.

7775 = 55555 in base 6.

7776 is a 5^{th} 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.

7851 = 7777 + 8 + 55 + 11.

7856 = 7777 + 8 + 5 + 66.

7905 is a Karmekar number in base 2.

7920 is the order of the smallest sporadic simple
group.

7936 is the 9^{th} 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 seven 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 Karmekar number in base 2.

8008 = _{16}C_{6}.

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.

8125 is the smallest number that can be written as
the sum of 2 squares in 5 ways.

8128 is the 4^{th} perfect 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 13^{th} power (besides
1).

8208 = 8^{4} + 2^{4} + 0^{4}
+ 8^{4}.

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.

8375 is the smallest number which has equal numbers
of every digit in bases 2 and 6.

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 = _{38}C_{3}.

8486 = 888 + 44 + 888 + 6666.

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 = _{18}C_{5}.

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.

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 4^{th}
powers.

8778 is a palindromic triangular number.

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

8833 = 88^{2} + 33^{2}.

8855 = _{23}C_{4}.

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.

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

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

9139 = _{39}C_{3}.

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

9189 is the number of sided 10-ominoes.

9240 = _{22}P_{3}.

9261 = 21^{3}.

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 19^{th} Lucas number.

9362 = 22222 in base 8.

9376 is automorphic.

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 divisors that contain
the digit 7.

9474 = 9^{4} + 4^{4} + 7^{4}
+ 4^{4}.

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.

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.

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.

9801 is 9 times its reverse.

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

9841 = 111111111 in base 3.

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

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

9880 = _{40}C_{3}.

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.

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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