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## 6214Re: [PrimeNumbers] Twin primes was: Infinite primes

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• Mar 30, 2002
--- David Litchfield <Mnemonix@...> wrote:
> > This is purported to be the original, although I fail to see why
> -1 wasn't
> > used instead.
>
> 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.
[...]
> That said in _reality_ q and r could both be composite - with two
> or more
> primes not in P1 to Pn being the factors.

could, and most of the time are.

> But then this is
> confusing reality
> with a hypothetical situtation

If you have the choice between reality and a hypothetical situation,
go with reality. Then there's no confusion.

> so does this proof for the twin
> prime
> conjecture stand in the same way the Euclid's proof is accepted.

It's not a proof, so it doesn't stand anywhere.

> At
> best
> this proves the twin prime conjecture - at worst it proves at least
> the
> possibility of an infinite number of twin primes.

Let e be a multiple of 6. Sometimes e+1 is prime. Sometimes e-1 is
prime.

The above "proves the possibility of an infinite number of twin
primes" to the same extent as your contruction. However, it doesn't
actually prove anything at all, as the whole thing about twins is the
simulaneity aspect, and that issue isn't addressed at all.
If predicate X(n) is satisfied for all even n, and predicate Y(n) is
statisfied for all odd n, even though there are an infinite number of
solutions to X and Y individually, we can't say _anything_ about the
likelyhood of simultanious satisfaction of X and Y.

Phil

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