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One hundred eleven

In mathematics, 111, or one hundred (and) eleven in base ten, is the natural number following one hundred ten and preceding one hundred twelve. It is R3 or the second repunit, a number like 11, 111, or 1111 that consists of repeated units, or 1's. It equals 3 x 37, therefore all triplets (numbers like 222 or 666) in base ten are of the form 3n x 37.

All triplets in all bases are multiples of 111 in that base, therefore the number represented by 111 in a particular base is the only triplet that can ever be prime. "111" is not prime in base ten, but is prime in base two, where 111 = 7 in base ten. It is also prime in these other bases 3 through 100: 3, 5, 6, 8, 12, 14, 15, 17, 20, 21, 24, 27, 33, 38, 41, 50, 54, 57, 59, 62, 66, 69, 71, 75, 77, 78, 80, 89, 90, and 99. 111 is also prime in base 111 (= 1243310).

The smallest magic square using only prime numbers (and 1) has a magic constant of 111:

31  73   7
13  37  61
67   1  43

A six-by-six magic square using the numbers 1 through 36 also has a magic constant of 111:

24  16  33  23  10   5
11  15  28   8  13  36
20  14   2  31  25  19
1  18   6  29  27  30
21  22   7  17  32  12
34  26  35   3   4   9

(The square has this magic constant because 1+2+3+...+34+35+36 = 666, and 666 / 6 = 111).

The number 111 is sometimes called a "nelson".

111 is also: