Re: Prime/Twin Prime Generator

• To: mathgroup at smc.vnet.net
• Subject: [mg103796] Re: Prime/Twin Prime Generator
• From: Chris Osborn <chrisosb at gmail.com>
• Date: Tue, 6 Oct 2009 08:02:04 -0400 (EDT)
• References: <ha9q8p\$7j7\$1@smc.vnet.net>

```On Oct 4, 4:35 am, Scott <sguth... at gmail.com> wrote:
> I'm under the delusion that I've come up with a way to recursively
> generate the primes and the twin primes. (I know, I know.) Anyway, the
> recursions are rendered in a Mathematica notebook and I'd be happy to
> pass it along (together with a paper describing the approach) to
> anybody that is interested (in the approach, not my delusion!).
>
> Cheers, Scott
> s... at acw.com

Hi Scott,

It seems that recursively generating the twin primes is quite doable.
You can just generate the natural numbers and select only the x where
x is prime and x + 2 is also prime.

If, however, you can prove that your algorithm will continue to
generate twin primes forever
(i.e. no matter how much you have generated so far, there is *always*
a future point where
your filter will find primes x and x + 2), then I think you will
have proved the twin prime conjecture.

I do not believe that having a recursive twin-prime generator will
make the proof of the twin prime
conjecture any easier, but I may be wrong.

Best,
Chris

```

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