Pillai prime
In number theory, 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 asked about these numbers. Their infinitude has been proved several times, by Subbarao, Erdős, and Hardy & Subbarao.
References
- Guy, R. K. (2004), Unsolved Problems in Number Theory (3rd ed.), New York: Springer-Verlag, p. A2, ISBN 0-387-20860-7.
- Hardy, G. E. & Subbarao, M. V. (2002), "A modified problem of Pillai and some related questions", American Mathematical Monthly 109 (6): 554–559, doi:10.2307/2695445.
- Pillai prime at PlanetMath.org.
| ||||||||||||||||||||||||||||||||||||||||||||||