EVERY NUMBER HAS A CONCEPT
0 is the additive identity.
1 is the multiplicative identity .
2 is the only even prime.
3 is the number of spatial dimensions we livein.
4 is the smallest number of colors sufficient tocolor all planar maps.
5 is the number of Platonic solids .
6 is the smallest perfect number.
7 is the smallest number of sides of a regular polygon that is not constructible by straightedge and compass.
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 Archimedean solids .
14 is the smallest even number n with no solutions to φ(m) = n.
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 x y = y x with x and y being different integers .
17 is the number of wallpaper groups .
18 is the only positive number that is twice the sum of its digits.
19 is the maximum number of 4 th 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 positive squares .
26 is the only positive 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 non-trivial 5th power.
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 non-trivial number which is both square and triangular.
37 is the maximum number of 5 th 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 a value of n so that x 2 + x + n takes on prime values for x = 0, 1, 2, ... n-2.
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 9×9 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 5×5 Latin squares .
57 = 111 in base 7.
58 is the number of commutative semigroups of order 4.
59 is the number of stellations of an icosahedron .
60 is the smallest number divisible by 1 through 6.
61 is the 3rd secant 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 2-digit string that appears latest in the decimal expansion of π .
69 is a value of n where n2 and n3 together contain each digit once.
70 is the smallest weird number .
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 multi-digit number which is one less than twice its reverse.
74 is the number of different non- Hamiltonian polyhedra with a 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 strongly connected digraphs with 4 vertices.
84 is the largest order of a permutation of 14 elements.
85 is the largest n for which 1 2+22+3 2+ ... +n 2 = 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 one of only 2 numbers 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 8×8 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...
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