Wilson定理是初等数论中的著名定理,文[1]证明了其逆定理也成立,但证明较复杂,本文用反证法给出一个简短的证明.Wilson定理之逆:若(p-1)!+1≡0(mod p),则p是素数.证明假设p不是素数,那么p一定可以分解素因数,令p1是p的一个真素因数,则1p1p-1,故p1(p-1)!,因此(p-1)!+1≡1(mod Wilson Theorem is a well-known theorem in elementary number theory. The paper [1] proves that the inverse theorem is also true, but the proof is more complicated. This paper uses contradiction to give a brief proof. Inverse of Wilson theorem: If (p-1)!+ 1≡0(mod p), then p is a prime number. Proof that p is not a prime number, then p must decompose the prime factor, so that p1 is a true factor of p, then 1p1p-1, so p1(p-1)! (p-1)!+1≡1(mod