# 31

This number is a prime.

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The smallest prime that starts a run of exactly four distinct primes that remain prime after each digit d is replaced by d^3: 31, 271, 83431, 5122764271. [Rivera]

31#/2 +/- 2 are the fourth and largest known (as of 2020) "cousin primes" of the type p#/2 +/- 2. (100280245063 and 100280245067). The other three pairs occur for p = 5, 7 and 13. [Rivera]

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