Wilson prime

If for a given prime $p$ it is true that $(p-1)!\\equiv-1\\mod p^{2}$ , then $p$ is called a Wilson prime. Like all other primes, Wilson primes satisfy the primality condition of Wilson’s theorem, but they also divide the Wilson quotient. Only three are known as of 2007, namely: 5, 13, 563 (A007540 in Sloane’s OEIS, which normally requires at least four terms before accepting sequences into the table). It is not known if there are infinitely many Wilson primes exist; the fourth Wilson prime would have to be greater than $10^{9}$ .

单词	WilsonPrime
释义	Wilson prime If for a given prime $p$ it is true that $(p-1)!\\equiv-1\\mod p^{2}$ , then $p$ is called a Wilson prime. Like all other primes, Wilson primes satisfy the primality condition of Wilson’s theorem, but they also divide the Wilson quotient. Only three are known as of 2007, namely: 5, 13, 563 (A007540 in Sloane’s OEIS, which normally requires at least four terms before accepting sequences into the table). It is not known if there are infinitely many Wilson primes exist; the fourth Wilson prime would have to be greater than $10^{9}$ .
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