It is given that Z = 31! X=31!+1 X+1=31!+2 this is divisible by 2 X+2=31!+3 this is divisible by 3 X+3=31!+4 this is divisible by 4 . . . . X+29=31!+30 this is divisible by 30 X+30=31!+31 this is divisible by 31 Hence, none of X+1,X+2,...,X+29,X+30 is a prime number Hence, option D is the correct answer.