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Old 2019-04-15, 16:11   #32
CRGreathouse
 
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Aug 2006

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Quote:
Originally Posted by MathDoggy View Post
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?

Last fiddled with by CRGreathouse on 2019-04-15 at 16:18
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