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# Pillai prime

If for a given prime $p$ we can find an integer $n>0$ such that $n!\equiv-1\mod p$ but $p\not\equiv 1\mod n$ then $p$ is a called a Pillai prime. These are listed in A063980 of Sloane’s OEIS. Sarinya Intaraprasert proved that there are infinitely many Pillai primes. The first few are 23, 29, 59, 61, 67, 71, 79, 83, 109, 137, 139, 149, 193, …

# References

- 1 R. K. Guy, Unsolved Problems in Number Theory New York: Springer-Verlag 2004: A2

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