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 (= 12433_{10}).
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 sixbysix 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).
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