JSH: Depressing reality, prime reality
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From: Tegiri Nenashi on 5 Mar 2010 21:58 On Mar 5, 6:08 pm, JSH <jst...(a)gmail.com> wrote: > ... So it could be decades now. Having reached 40 it occurs to me that I > don't have any juice left for major discoveries anyway. It is a young > person's game, and unfortunately mostly a young man's game... I find it strange -- sure you don't lack ambition. Why not to proclaim a goal: "I'm going to discover something important at 50?" (Of course, announcing such a goal on a newsgroup is the best way to ruin it -- discoveries are made in quiet libraries, and not noisy hallways).
From: fishfry on 6 Mar 2010 00:19 In article <5141d1da-1266-4345-80ff-94fd799b76e8(a)y7g2000prc.googlegroups.com>, JSH <jstevh(a)gmail.com> wrote: > There is a lot of satisfaction with having my own axiom, which I had > the honor of naming as I'm the discoverer, which is of course, the > prime residue axiom, and yes, posters can reply in the negative or > derisively, but there you see the difference between finding something > and talk. JSH I have been reading your stuff for years and you have truly flipped your wig.
From: fishfry on 6 Mar 2010 00:19 In article <5141d1da-1266-4345-80ff-94fd799b76e8(a)y7g2000prc.googlegroups.com>, JSH <jstevh(a)gmail.com> wrote: > > So it could be decades now. Having reached 40 it occurs to me that I > don't have any juice left for major discoveries anyway. Yeah there goes your Fields medal.
From: MichaelW on 6 Mar 2010 01:07 On Fri, 05 Mar 2010 18:08:46 -0800, JSH wrote: > There is a lot of satisfaction with having my own axiom, which I had the > honor of naming as I'm the discoverer, which is of course, the prime > residue axiom, and yes, posters can reply in the negative or derisively, > but there you see the difference between finding something and talk. > <snip> > > James Harris Just to cut short the usual abusive posting and get back to maths I took the "axiom" and used it to derive the following: Let p(k) be the k-th prime (for example p(5) = 11). The number of twin prime pairs up to (p(k))^2 trends to h*k^2 where h is a constant with a value of about 0.291. For example p(11)=31. The number of twin prime pairs to 31^2=961 is 35. The approximation above sets it at about 11^2*.291 = 35.211 which is a pretty good match. I have run up to p(1000) and charted the results and it does indeed appear to stay increasingly close to just over 0.29. I found this to be a surprising and cute result. I am sure it is known but have not been able to find a reference so if someone has seen this before could they let me know? Anyway the point is that there is some real working maths underlying James' work. Regards, Michael W.
From: Mark Murray on 6 Mar 2010 06:37
On 06/03/2010 06:07, MichaelW wrote: > Anyway the point is that there is some real working maths underlying > James' work. Does James add anything to Dirichlet's Theorem? http://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions M -- |