JSH: Twin primes
in [Math]
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From: JSH on 1 Feb 2010 00:37 On Jan 31, 8:58 pm, Joshua Cranmer <Pidgeo...(a)verizon.invalid> wrote: > On 01/31/2010 11:29 PM, JSH wrote: > > > On Jan 31, 8:11 pm, Joshua Cranmer<Pidgeo...(a)verizon.invalid> wrote: > >> With the exception of the 13-17 range, your predicted number proves to > >> be higher than the actual. I didn't have a larger list of twin primes to > > > Meaningless. It's a probability result. > > The deviations should be normally distributed about 0. I'm pointing out > that they certainly don't *seem* to be, although 10 points is a bit > scant to make certain accusations, especially as I don't care to do a > proper statistical hypothesis test right now. The result follows from a proof which is based on what I now call the prime residue axiom, which states that primes do not have a preference for a residue modulo another prime. Your position is like a person noticing ten coin flips that are heads who wants to know if the coin is fair, as that seems really unlikely. But it can happen as anyone who flips a coin a lot knows. But that's human nature. Your brain craves patterns. > >> If you were serious about this work, why not code a program that checks > >> the predicted and actual value of twin primes for the first few hundred > >> of them? Extrapolating based on a few low values does not make a > >> compelling argument. > > > Wouldn't matter. There's too much research money in this area and the > > twin primes conjecture is too famous. > > That is a... naive view. I can't say that I've ever met a researcher so > egotistical they would actively withhold research merely to keep > research money. I've talked about this result before. I had it over 3 years ago. It doesn't matter what I discover. The reaction is always the same. > > The math community will not allow me to get research acceptance here > > any more than with all my other research results. > > Your other research results which seem to have been, in general, at best > poorly written and explained and at worst outright incorrect. Like my twin primes probability result? > > Why don't I just go ahead and prove or disprove the Riemann Hypothesis > > with my prime counting function? Why don't I just use my quadratic > > residue results to try and make a factoring program? Why don't I just > > implement my optimal path algorithm and see if it really does solve > > the traveling salesman problem? > > The algorithm whose incorrectness I demonstrated thrice? Well you better hope you did. Another person said he proved it wrong as well. I haven't checked it. But if it does work then you can end up defined by nothing else but your vocal rejection. If that algorithm does work then it has a value to the world that is incalculable. Claiming it wrong and being wrong would be like trying to stop people from ever learning calculus. Knowledge is funny that way. People like you think here is some kind of personal battle. But when I'm right you're fighting humanity. That's not a nice thing to do. > > I defined mathematical proof. I discovered tautological spaces. > > > I gave the best general method for simplifying binary quadratic > > diophantine equations. > > And I help develop widely-used software and have inadvertently > publicized minor new features (I did not expect that post to be so > widely distributed....). If I were more egotistical, I could also > stretch my claims to say the development of a full static analysis > toolkit (only a framework to build upon, and incomplete at that). And if you hadn't? If just my optimal path algorithm is correct then it can mean more rapid technological advances, for the entire world. Ok, you say it's wrong. I hope you're right. As if you are wrong then you may have destroyed your future career and I really do not know exactly why you have. > > Your opinion of me is as irrelevant as your ignorance of the > > mathematics I understand. > > ... Newton once said, "If I have seen a little further, it is by > standing on the shoulders of giants." Could you be as humble as him? Newton shredded his foes. He was known during his time as a person you did not cross. Later on he was in charge of the mint and had counterfeiters executed. History picks and chooses. It also re-writes as it sees fit. If you knew Newton the man, you would probably hate him. You certainly would not call him humble. > > You need bogus math to pay the bills. I don't. > > I'm not a paid mathematician, and the last job I had that involved > moderately complex mathematics was almost four years ago. I'm sure > that's true of most people in this forum: most professors probably don't > have the time to read newsgroups, and certainly not to respond. Which is why YOU for a moment acted as if the twin primes result was interesting. I was talking about the people who do need it, to pay the bills. My optimal path algorithm is fun to me. I like it. I have no more motivation to use it to force the issue with the traveling salesman problem than I need to try and use the twin primes result, as I know how fiercely people fight when their livelihoods are threatened. Quite a few math people do fake math. They lie about what they're doing and the world lets them, for now. But when it stops, make no mistake, these people will fight to keep the money flowing. And when they lose, they'll be angry. The truth is for the people who can afford it. James Harris
From: Tim Little on 1 Feb 2010 01:24 On 2010-02-01, JSH <jstevh(a)gmail.com> wrote: > The result follows from a proof which is based on what I now call > the prime residue axiom, which states that primes do not have a > preference for a residue modulo another prime. What you don't know is whether your axiom is consistent with the others. If it is not, then any proof based on it is useless. - Tim
From: Mark Murray on 1 Feb 2010 04:28 On 01/02/2010 05:37, JSH wrote: >> Your other research results which seem to have been, in general, at best >> poorly written and explained and at worst outright incorrect. > > Like my twin primes probability result? Yes. >>> Why don't I just go ahead and prove or disprove the Riemann Hypothesis >>> with my prime counting function? Why don't I just use my quadratic >>> residue results to try and make a factoring program? Why don't I just >>> implement my optimal path algorithm and see if it really does solve >>> the traveling salesman problem? >> >> The algorithm whose incorrectness I demonstrated thrice? > > Well you better hope you did. Another person said he proved it wrong > as well. > > I haven't checked it. You never do. > But if it does work then you can end up defined by nothing else but > your vocal rejection. > > If that algorithm does work then it has a value to the world that is > incalculable. "If". > Claiming it wrong and being wrong would be like trying to stop people > from ever learning calculus. > > Knowledge is funny that way. People like you think here is some kind > of personal battle. > > But when I'm right you're fighting humanity. > > That's not a nice thing to do. Try to write sense, man! Rest of utterly nonsensical verbiage elided. M
From: Jesse F. Hughes on 1 Feb 2010 06:25 Tim Little <tim(a)little-possums.net> writes: > On 2010-02-01, JSH <jstevh(a)gmail.com> wrote: >> The result follows from a proof which is based on what I now call >> the prime residue axiom, which states that primes do not have a >> preference for a residue modulo another prime. > > What you don't know is whether your axiom is consistent with the > others. If it is not, then any proof based on it is useless. > It's a little odd to think that the guy who defined mathematical proof doesn't know what an axiom is, huh? -- Jesse F. Hughes "I think the problem for some of you is that you think you are very smart. I AM very smart. I am smarter on a scale you cannot really comprehend and there is the problem." -- James S. Harris
From: MichaelW on 1 Feb 2010 09:42
On Feb 1, 3:29 pm, JSH <jst...(a)gmail.com> wrote: > On Jan 31, 8:11 pm, Joshua Cranmer <Pidgeo...(a)verizon.invalid> wrote: > > > > > > > On 01/30/2010 01:53 PM, JSH wrote: > > > > So let's try it out. Between 5^2 and 7^2, there are 6 primes. The > > > probability then is given by: > > > > prob = ((5-2)/(5-1))*((3-2)/(3-1) = (3/4)*(1/2) = 0.375 > > > > And 6*0.375 = 2.25 so you expect 2 twin primes in that interval. > > > The primes are 29, 31, 37, 41, 43, 47 and you'll notice, two twin > > > primes as predicted: 29,31 and 41, 43. > > > So let's try it out more: > > Range primes prob predict actual > > 3- 5 5 .5 -> 2.50 2 > > 5- 7 6 .375 -> 2.25 2 > > 7-11 15 .3125 -> 4.69 4 > > 11-13 9 .28125 -> 2.53 2 > > 13-17 22 .257813 -> 5.67 7 > > 17-19 11 .241699 -> 2.66 2 > > 19-23 27 .228271 -> 6.16 4 > > 23-29 47 .217896 -> 10.24 8 > > 29-31 16 .210114 -> 3.36 2 > > 31-37 57 .203110 -> 11.58 11 > > > With the exception of the 13-17 range, your predicted number proves to > > be higher than the actual. I didn't have a larger list of twin primes to > > Meaningless. It's a probability result. > > Human nature is to try and find patterns in random, but it's just a > brain habit. > > > count the actual numbers, so this table stops at 37, which is before > > what I think would be the interesting ranges 47-53 (the first pair of > > numbers where neither is a twin prime) and 59-61 (the first pair of twin > > primes after that). If you notice, 23 (the first non-twin prime) is > > involved in the two most "egregious" overestimates. > > By the prime residue axiom the primes DO NOT CARE about their residue > modulo another prime so it's true randomness. There is no reason in > it. > > Here's a bigger example: > > The probability that for a prime between 97^2 and 100^2 that adding 2 > to it gives a prime is about 15.58% and there are 66 primes in that > interval so there should be about 10 twin primes, and a quick count > shows that there are: > > (9419, 9421), (9431, 9433), (9437, 9439), (9461, 9463), (9629, 9631), > (9677, 9679), (9719, 9721), (9767, 9769), (9857, 9859), (9929, 9931) > This example struck me as rather convenient. For example if the range is from 113^2 to 116^2 then the prediction is under 11 twins but the actual count is 7. I suspect James is being selective. I have written a program and looking at the results between 100 and 200 the match varies from really good (139^2 to 146^2 gets the correct answer (30) within 1%) to the really bad (157^2 to 163^2 predicts 27 but there are only 17). Using values betwen 100 and 200 I get a prediction within 20% of the right value about 60% of the time (roughly). Regards, Michael W. |