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]