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