The number of primes Sigma(n)(i=1)(-1)(n-i)i! is finite

For a positive integer n let A(n+1) = Sigma(i=1)(n) (-1)(n-i)i!, !n = Sigma (i=0)(n-1) i! and let p(1) = 3612703. The number of primes of the form A(n) is finite, because if n greater than or equal to p(1), then A(n) is divisi ble by p(1). The heuristic argument is given by which there exists a prime p such that p \ !n for all large n; a computer check however shows that thi s prime has to be greater than 2(23). The conjecture that the numbers !n ar e squarefree is not true because 54503(2)\ !26541.