There are no socialist primes less than 10^9

Abstract

There are no primes $p$ with $5<p<10^{9}$ for which $2!, 3!, \ldots, (p-1)!$ are all distinct modulo $p$; it is conjectured that there are no such primes.

4 pages; some typos corrected in version 3 and some more references added; computational range extended in version 2