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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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## Mathematics Subject Classification

11A41*no label found*

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new correction: examples and OEIS sequences by fizzie

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new correction: Define Galois correspondence by porton

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new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

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new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith