- Mar 30, 2002
> This is purported to be the original, although I fail to see why -1 wasn't

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

> used instead.

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

q - r = 2.

What's more as twin primes must be +1 or -1 an even multiple of 3 (due to

the location and frequency of multiples of three : the only possible place

for twin primes is either side of 2*3*n) then P1 * P2 * .... Pn should be an

even multiple of 6 if indeed r and q are twin primes.

As P1 = 2 and P2 = 3 then P1*P2*...Pn must be an even multiple of 3 - so

fulfulling the "twin primeness" of r and q.

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.

TIA,

David Litchfield

----- Original Message -----

From: "Jon Perry" <perry@...>

To: "Prime Numbers" <primenumbers@yahoogroups.com>

Sent: Saturday, March 30, 2002 9:12 AM

Subject: RE: [PrimeNumbers] Infinite primes

>

> There is an interesting paper that covers various proofs of the infinitude

> of primes at:

>

> http://algo.inria.fr/banderier/Seminar/Vardi/index.html

>

> Jon Perry

> perry@...

> http://www.users.globalnet.co.uk/~perry/maths

> BrainBench MVP for HTML and JavaScript

> http://www.brainbench.com

>

>

> -----Original Message-----

> From: David Litchfield [mailto:Mnemonix@...]

> Sent: 29 March 2002 22:40

> To: Prime Numbers

> Subject: [PrimeNumbers] Infinite primes

>

>

> I know Euclid proved there were an infinite number of primes. Was this his

> proof?

>

> Assume there are a finite number of primes - P1, P2, P3....Pn

>

> q = P1 * P2 * P3 * .... Pn + 1

>

> q divided by any of Px always leaves a remainder of 1 and therefore q must

> also be prime and as q was not one of P1 to Pn then there are an infinite

> number of primes.

>

> I know Ribenboim and Kummer produced proofs that were variants of Euclid's

> proof - I'm just wondering if the above was the original?

>

> TIA,

> David

>

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