## Re: [PrimeNumbers] Twin primes was: Infinite primes

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• ... 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
Message 1 of 3 , Mar 31, 2002
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