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There are no socialist primes less than 10^9

Number Theory 2015-07-02 v3
Authors: Tim Trudgian
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Abstract

There are no primes pp with 5<p<1095<p<10^{9} for which 2!,3!,…,(p−1)!2!, 3!, \ldots, (p-1)! are all distinct modulo pp; it is conjectured that there are no such primes.

Keywords

socialist primes factorials modular arithmetic prime numbers conjecture

Cite

@article{arxiv.1310.6403,
  title  = {There are no socialist primes less than 10^9},
  author = {Tim Trudgian},
  journal= {arXiv preprint arXiv:1310.6403},
  year   = {2015}
}

Comments

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

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