6.- Conjecture .
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From: Ludovicus on 28 Jul 2010 10:34 "Given an even number N, if we subtract from it the odd primes 3,5, 7...p(n) then the number n of primes needed for obtaining the first prime difference will be ever less than 0.72*(Ln N)^2" Example: Be N = 3807404, its necessary to subtract to the 132th prime , to obtain a prime difference. 3807404 - 751 = 3806653 = prime . ..72*(ln 3807404)^2 = 165 > 132. Ludovicus
From: hagman on 28 Jul 2010 13:10 On 28 Jul., 16:34, Ludovicus <luir...(a)yahoo.com> wrote: > "Given an even number N, if we subtract from it the odd primes 3,5, > 7...p(n) > then the number n of primes needed for obtaining the first prime > difference > will be ever less than 0.72*(Ln N)^2" > Example: Be N = 3807404, its necessary to subtract to the 132th > prime , > to obtain a prime difference. 3807404 - 751 = 3806653 = prime . > .72*(ln 3807404)^2 = 165 > 132. > Ludovicus First show that such n exists at all.
From: Gerry Myerson on 28 Jul 2010 19:39 In article <c76898e8-2155-4da4-ac59-c8edab11a8be(a)f6g2000yqa.googlegroups.com>, hagman <google(a)von-eitzen.de> wrote: > On 28 Jul., 16:34, Ludovicus <luir...(a)yahoo.com> wrote: > > "Given an even number N, if we subtract from it the odd primes 3,5, > > 7...p(n) > > then the number n of primes needed for obtaining the first prime > > difference > > will be ever less than 0.72*(Ln N)^2" > > Example: Be �N = 3807404, its necessary to subtract �to the 132th > > prime , > > to obtain a prime difference. �3807404 - 751 = 3806653 �= prime . > > .72*(ln 3807404)^2 = 165 > 132. > > Ludovicus > > First show that such n exists at all. Then collect your Fields medal. -- Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
From: Ludovicus on 30 Jul 2010 13:11 > > On 28 Jul., 16:34, Ludovicus <luir...(a)yahoo.com> wrote: > > > "Given an even number N, if we subtract from it the odd primes 3,5, > > > 7...p(n) > > > then the number n of primes needed for obtaining the first prime > > > difference > > > will be ever less than 0.72*(Ln N)^2" > > First show that such n exists at all. > Then collect your Fields medal. > Gerry Myerson Good. Then your answer is: "That is a very hard conjecture"
From: Gerry on 30 Jul 2010 19:00
On Jul 31, 3:11 am, Ludovicus <luir...(a)yahoo.com> wrote: > > > On 28 Jul., 16:34, Ludovicus <luir...(a)yahoo.com> wrote: > > > > "Given an even number N, if we subtract from it the odd primes 3,5, > > > > 7...p(n) > > > > then the number n of primes needed for obtaining the first prime > > > > difference > > > > will be ever less than 0.72*(Ln N)^2" > > > First show that such n exists at all. > > Then collect your Fields medal. > > Gerry Myerson > > Good. Then your answer is: "That is a very hard conjecture" Showing that n exists is a notoriously hard conjecture. Showing that it need never exceed your bound, I don't know; if it's true, it's certainly hard, but if it's false, maybe someone has already found a counterexample. A lot of computational work has been done on Goldbach, I'm sure you can find relevant stuff online. -- GM |