Pillai prime
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A Pillai prime is a prime number p for which there is an integer n > 0 such that the factorial of n is one less than a multiple of the prime, but the prime is not one more than a multiple of n. To put it algebraically, 
but 
. The first few Pillai primes are
Pillai primes are named after the mathematician Subbayya Sivasankaranarayana Pillai, who proved that there are infinitely many Pillai primes.
[edit] References
- R. K. Guy, Unsolved Problems in Number Theory New York: Springer-Verlag 2004: A2
- G. E. Hardy and M. V. Subbarao, "A modified problem of Pillai and some related questions", Amer. Math. Monthly 109 6 (2002): 554 - 559.
- Pillai prime on PlanetMath
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