Quote:
Originally Posted by MathDoggy
A factorial number x! of a positive integer is divisible by every integer from 2 to x, inclusive. Hence, x!+1 is either a twin prime number or divisible by a prime larger than x. In either case, for every positive integer x, there is a least one twin prime bigger than x.
The conclusion is that there exist infinitely many twin prime numbers.

How does "divisible by a prime larger than x" show that there is a twin prime bigger than x?