# 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, ${\displaystyle n!\equiv -1\mod p}$ but ${\displaystyle p\not \equiv 1\mod n}$. The first few Pillai primes are