Every once in awhile, I come across a video (usually on Youtube, isn’t that where everthing ends up) that quite elegantly illustrates something math-related. I haven’t been collecting them long, but I thought I’d share a couple of them with you all. Please enjoy them as much as I have.

Someone over at Stetson University1 has compiled a list of numbers2 with the reasons they might be termed “special”. Some of these reasons are out there, and maybe a little contrived, but I’ve found a few that I like. Take some time to browse this list, and I’m sure you’ll find something of interest. If not, check out the the entire list.


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 faces of a regular polygon that is not constructible by straightedge and compass.
8 is the largest cube in the Fibonacci sequence.
12 is the smallest abundant number.
13 is the number of Archimedian solids.
18 is the only number (other than 0) that is twice the sum of its digits.
25 is the smallest square that can be written as a sum of 2 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.
31 is a Mersenne prime.
38 is the last Roman numeral when written lexicographically.
40 is the only number whose letters are in alphabetical order.
42 is the 5th Catalan number.3
46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9×9 chessboard.
53 is the only two digit number that is reversed in hexadecimal.
55 is the largest triangular number in the Fibonacci sequence.
65 is the smallest number that becomes square if its reverse is either added to or subtracted from it.
70 is the smallest weird number.
109 has a 5th root that starts 2.555555….
110 is the smallest number that is the product of two different substrings.
128 is the largest number which is not the sum of distinct squares.
132 is the smallest number which is the sum of all of the 2-digit numbers that can be formed with its digits.
135 = 11 + 32 + 53.
145 = 1! + 4! + 5! (a factorion).
151 is a palindromic prime.
153 = 13 + 53 + 33.
198 = 11 + 99 + 88.
200 is the smallest number which can not be made prime by changing one of its digits.
210 is the product of the first 4 primes.
257 is a Fermat prime.
536 is the number of solutions of the stomachion puzzle.
540 is divisible by its reverse.
668 is the number of legal pawn moves in Chess.
762 is the starting location of 999999 in the decimal expansion of p.
873 = 1! + 2! + 3! + 4! + 5! + 6!
901 is the sum of the digits of the first 100 positive integers.
976 has a square formed by inserting a block of digits inside itself.
1229 is the number of primes less than 10000.
1233 = 122 + 332.
1369 is a square whose digits are non-decreasing.
1620 is a highly abundant number.
1933 is a prime factor of 111111111111111111111.
2239 is a prime that remains prime if any digit is deleted.
2997 = 222 + 999 + 999 + 777.
3094 = 21658 / 7, and each digit is contained in the equation exactly once.
3313 is the smallest prime number where every digit d occurs d times.
4013 is a prime factor of 1111111111111111111111111111111111.
4725 is an odd abundant number.
4913 is the cube of the sum of its digits.
5471 contains no 0′s in base 3 through base 10.
5689 is the largest 4-digit prime with strictly increasing digits.

What an awesome list, thanks!


The Count

1. Stetson University
2. What’s special about this number?
3. Besides being … you know … the answer to Life, the Universe, and Everything.