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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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new image: plot W(t) = P(waiting time <= t) by robert_dodier

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier