Revising history

One of the three numbers $X-2,X-1,X+1$ must be even. The only even prime number is $2$ . So, one of them is $2$ , while the other two are odd. The only such triple is $2,3,5$ . Hence $X-2=2\implies X=\boxed 4$ .

We know after every even number, an odd number comes then another even number and so on, i.e a consecutive set of numbers contains some even numbers and odd numbers. $X-2, X-1, X, X+1$ are 4 consecutive numbers so 2 out of them must be odd and the other 2 must be even. The only even prime number is 2, so if $X-1$ was 2 then $X+1$ would be even as alternate numbers have the same parity but it can't be as $X+1$ is prime, $X-2$ must be 2.

$X-2=2$ $X=4$