A Pillai prime is a type of prime number characterized by its relationship to the factorial function. Specifically, a Pillai prime \( p \) is defined as a prime number for which there exists a positive integer \( n \) such that \( n! \equiv -1 \mod p \). This means that when \( n! \) (the factorial of \( n \)) is divided by the prime \( p \), it leaves a remainder of \( p - 1 \).
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