improved sieve of erastothenes
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From: luiroto on 20 Dec 2006 21:33 Phil Carmody ha escrito: > luiroto(a)yahoo.com writes: > > JAVIER RAMOS HERMAN ha escrito: > > > I think that close study of the 6n-1 and 6n+1 series and the sieving frequencies can lead to the proof that twin prime numbers are infinite. >> > Too much optimist. > > THat bit's true. > > > On the contrary, the coincidence of two primes in > > the sequences 6n+1 and 6n-1 throws the problem to probability > > calculus, that is, out of deterministic mathematics. > > But that's hovering between wrong and meaningless. > > It's entirely deterministic, we just don't have the methods for > concluding the result that we desire yet. The techniques used nowadays > may be analytic rather than discrete, but that doesn't mean that > the results are somehow not absolute. > Phil As Javier spoke of "sieving frequencies" I made reference to probability. Really it is deterministic, but I think the sequence of primes is a Chaotic Recursive Sequence, that is: unpredictable.Then it is perfectly possible that the conjecture be false. Ludovicus
From: JAVIER RAMOS HERMAN on 9 Jan 2007 02:02 this algorithm just allows to sieve without multiples of 2 and 3. sorry if you do not understand the meaning of sieving frequencies. i thought it was clear. what do you not understand about them? i know twin prime numbers are infinite because i have worked with this recursive structure of prime numbers for a while we know than prime numbers are infinite. this means that there is an infinitude of prime numbers in the form 6*n-1 and in the form 6*n+1 aswell. a pair of twin prime numbers occurs when for a specific symetry both series have not been sieved if there is an infinitude of prime numbers with the symetry of the sieve for 6*n-1 and 6*n+1 it seems clear that there is an infinitude of twin prime numbers in other words if prime numbers are infinite then twin prime numbers are also infinite. i know this is no proof that's why i posted this improved sieve. i hope than we together can prove it
From: JAVIER RAMOS HERMAN on 9 Jan 2007 02:07
Re: improved sieve of erastothenes Posted: Dec 20, 2006 9:33 PM Plain Text Reply Phil Carmody ha escrito: > luiroto(a)yahoo.com writes: > > JAVIER RAMOS HERMAN ha escrito: > > > I think that close study of the 6n-1 and 6n+1 series and the sieving frequencies can lead to the proof that twin prime numbers are infinite. >> > Too much optimist. > > THat bit's true. > > > On the contrary, the coincidence of two primes in > > the sequences 6n+1 and 6n-1 throws the problem to probability > > calculus, that is, out of deterministic mathematics. > > But that's hovering between wrong and meaningless. > > It's entirely deterministic, we just don't have the methods for > concluding the result that we desire yet. The techniques used nowadays > may be analytic rather than discrete, but that doesn't mean that > the results are somehow not absolute. > Phil As Javier spoke of "sieving frequencies" I made reference to probability. Really it is deterministic, but I think the sequence of primes is a Chaotic Recursive Sequence, that is: unpredictable.Then it is perfectly possible that the conjecture be false. Ludovicus please work with the algorithm either for hp 48 or the c++ version to get a touch with the improved sieve. you will then see that prime numbers can be defined with a recursive structure thank you for your comments javier |