8933

This number is a prime.

+ In the race for most appearances by a digit in the first n primes, the four prime digits (2,3,5,7) tie for an early lead but soon lose it to 1 which stays in the lead or tied for the lead until, ironically, the 1111th prime (8933) at which point the digit 3 pulls ahead 623 to 621. [Gaydos]

+ The least prime p that is a substring of (p-1) * p * (p+1). E.g. 8932 * 8933 * 8934 = 712839893304 and 8933 is a substring. [Lava]

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