How to prove N+2k, k>1 Primes are infinite? #657 Correcting Math
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From: Archimedes Plutonium on 12 Jul 2010 19:16 Archimedes Plutonium wrote: (snipped) > But that is sufficient to prove the infinitude of Quad primes and all > primes of form N + 2k > for k>1. I say this because to have only Regular Primes infinite and N > +2 primes infinite > but to have N+4, N+6, etc etc as all finite sets of primes is a > contradiction. Whether a contradiction of the Prime distribution > theorem or some other distribution of primes theorem > I am not quite sure as yet. > > What I suspect is that given the information that Twin Primes is an > infinite set, makes the > proposition that all N+2k, k>1 sets of primes must also be infinite. > I guess noone thought that if you prove the Infinitude of Twin Primes, that it was much of use for anything. That it was a one item proof that had no value elsewhere. That nothing else hinged on whether Twin Primes were infinite or finite. But I suspect that a proof of Infinitude of Twin Primes is the access door to proving the infinitude of N+2k, k>1 sets of Primes, such as the Quad Primes. So all I have to do is find a theorem in math that I can contradict that theorem when the input is that Regular primes are infinite and Twin primes are infinite and unless all primes of form N+2k, k>1 are infinite that such and such a theorem is contradicted. I hope that is not the Riemann Hypothesis. I was thinking of something much smaller of a theorem such as the theorem that between N and 2N must always exist at least one prime number. So that if Regular Primes are infinite and Twin Primes are infinite, then N+4, N+6, N+8, N+10, etc etc must all be infinite sets also, or else we contradict a theorem. Mathematics is not asymmetrical like this. Where you have Twin primes as infinite yet the others finite. That makes little sense. Archimedes Plutonium http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |