Burt Kaliski Jr. (@modulomathy)

4/20/12 5:23 PM

#math trivia for #April20: #111 is a prime in every base less than 10, except for which two?

The base-10 values corresponding to 111 in bases 1 to 9 are

3,7,13,21,31,43,57,73,91

There are actually three non-primes in this list, the ones corresponding to bases 4, 7, and 9. I should count more carefully when making up the problems! But it is still interesting that two thirds of the values are prime. They’re all odd, which does increase their probability of being prime, but only about half of the odd numbers up to 91 are prime, and here we have a set where two thirds of them are.

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