This is bit faster:
toPrime = 500; sums = Accumulate@FoldList[#1 #2 &Accumulate@FoldList[Times, 1, Range[2, Prime@toPrime - 1]]; primes = Prime[Range[toPrime]]; Mod[sums[[primes - 1]], primes] Precompute factorial sums and primes. Mod is fast on lists.