2011/011) what is the smallest prime factor of 2010! +1

As per Wilson's theorem for prime p

(p- 1)! = - 1 mod p

as as 2011 is a prime number

2010 ! = - 1 mod 2011

so 2011 is a factor of 2010 ! + 1

and as 2 to 2010 cannot divide it so smallest prime factor is 2011