David Litchfield <

Mnemonix@...>wrote:

> Yep. The reason I ask was because this could prove the twin prime

> conjecture.

>

> If q= P1 * P2 * ... Pn + 1

>

> then q is prime because q mod and Pn is 1.

> Using the same logic, it also follows that

>

> r = P1 * P2 * .... Pn -1

>

> is also prime because r mod any Pn equals Pn-1

So there a contradiction, and the number of primes is infinite.

It is not to say that indeed q and r both are prime , otherwise, you wold

prove the twin prime conjecture

> q - r = 2.

> That said in _reality_ q and r could both be composite - with two or more

> primes not in P1 to Pn being the factors. But then this is confusing reality

> with a hypothetical situtation so does this proof for the twin prime

> conjecture stand in the same way the Euclid's proof is accepted. At best

> this proves the twin prime conjecture - at worst it proves at least the

> possibility of an infinite number of twin primes.

But then this is not confusing reality with a hypothetical situtation , it is you are

confusing your logic.

Liu Fengsui