Is 2010 factorial + 1 prime? 2! + 1 = 3 is prime 3! + 1 = 7 is prime 4! + 1 = 25 = 5 × 5 is not prime 5! + 1 = 121 = 11 × 11 is not prime 6! + 1 = 721 = 7 × 103 is not prime 7! + 1 = 5041 = 71 × 71 is not prime 8! + 1 = 40321 = 61 × 661 is not prime

Is 2010 factorial + 1 prime? 2! + 1 = 3 is prime 3! + 1 = 7 is prime 4! + 1 = 25 = 5 × 5 is not prime 5! + 1 = 121 = 11 × 11 is not prime 6! + 1 = 721 = 7 × 103 is not prime 7! + 1 = 5041 = 71 × 71 is not prime 8! + 1 = 40321 = 61 × 661 is not prime

A deduction from Wilson's theorem:
When p is prime, (p-1)! + 1 must have a factor P
And 2011 is a prime number, so (2011-1)! + 1 must have a factor 2011
So 2010! + 1 is not prime