## 6213Twin primes was: Infinite primes

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• 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
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@...>
Sent: Saturday, March 30, 2002 9:12 AM

>
> 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
>
>
> 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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