JSH: Twin primes
in [Math]
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From: David C. Ullrich on 2 Feb 2010 06:33 On Sun, 31 Jan 2010 17:04:44 EST, master1729 <tommy1729(a)gmail.com> wrote: >David C Ullrich said : > >> On Sat, 30 Jan 2010 10:53:17 -0800 (PST), JSH >> <jstevh(a)gmail.com> >> wrote: >> >> >One of the weirder things I discovered a while back >> was a resistance >> >to probabilistic explanations for some prime things >> where the easiest >> >area to see it boldly displayed is with twin primes >> probability. >> >> As discoveries go that's certainly "weird", mainly >> becasue it's not >> true. >> >> Mathematicians don't "resist" probabilistic arguments >> about primes; >> they're big fans of such things. As hints regarding >> what might be >> true. >> >> Of course they do "resist" the idea that such >> arguments actually >> _prove_ things about primes. Because they don't prove >> anything, >> because the primes are not actually random in any >> sense that >> would make those arguments into actual proofs. >> > >Indeed. I fully agree. > >JSH might have a good argument , but no proof. >(as i said before ... and btw i do have a proof ) No doubt you do. And you haven't shown it to anyone because, um,... Ah, got it. You haven't shown it to anyone because imagining you have a proof is more fun than discovering it's wrong. > >your not a fan of me , but im glad we agree on this. > >i dont like opponents but at least your not a 'moran' :) > >regards > >tommy1729 > >> >To understand fully, imagine that you accept that >> primes don't have a >> >preferred residue modulo themselves with other >> primes. For instance, >> >3 has two potential residues modulo other primes: 1 >> and 2. Should it >> >prefer 1? Or maybe 2? No. Why would 3 care to >> lean towards either >> >residue? >> > >> >If so, then what residue a particular prime has mod >> 3 should be >> >random. >> > >> >Ok, so now let's get to twin primes. >> > >> >Here a trivial little result relating to twin primes >> as if x is prime >> >and greater than 3 the probability that x+2 is prime >> is given by: >> > >> >prob = ((p_j - 2)/(p_j -1))*((p_{j-1} - 2)/(p_{j-1} >> - 1))*...*(1/2) >> > >> >where j is the number of primes up to sqrt(x+2), and >> p_j is the jth >> >prime, p_{j-1} is the prime before it and so forth. >> > >> >The result is easy as it is just multiplying the >> probability for each >> >prime that it is NOT true that >> > >> >x + 2 ? 0 mod p >> > >> >which probability is just the result of dividing one >> minus the number >> >of non-zero residues by the total number of residues >> together to get >> >the total probability that a prime plus 2 is also >> prime. >> > >> >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 that's a fun little thing where you can calculate >> easily when >> >you're bored or something and it works crazy well. >> Where it is all >> >just about a simple little idea that prime numbers >> aren't picking in >> >this simple way, and some of you of course know that >> what I've given >> >looks like a piece of Brun's constant. >> > >> >Now I noticed that years ago and wondered why math >> people don't then >> >accept then that it's about probability with twin >> primes, when they >> >HAVE the probability piece ALREADY in an accepted >> bit of mathematics, >> >and one answer may be that a simple answer is just >> not wanted. >> >I found that sad. But it was one of the results >> that gave me >> >perspective about my other research where I found >> simple answers and >> >math people wouldn't accept the results as if you >> look across the >> >research in this area you see a LOT of people with >> funding to do >> >research in an area where the simple answer means >> they cannot succeed >> >with anything more complex. >> > >> >They cannot succeed. >> > >> >You now know that without having to know complex >> mathematical ideas! >> >Wow, just like that you're at the top of the field >> and can shoot down >> >Ph.D's with decades as mathematicians if one of them >> pretends to >> >produce a twin primes conjecture result. >> > >> >Given that they cannot succeed they can fund their >> research >> >indefinitely simply by ignoring the simple answer. >> > >> >So it's a cash cow. >> > >> >Oh yeah, so if you figure that twin primes don't >> care about their >> >residue modulo other primes so they just randomly >> bounce around by >> >residue then you know the answer to the Twin Primes >> Conjecture. It's >> >true. >> > >> >Another way to say it is that prime numbers will >> never hate p_1 mod >> >p_2 = 2, so that will emerge when p_1 > p_2 simply >> because the primes >> >don't have a reason to start dropping that >> possibility, so there will >> >always be twin primes. Easy. >> > >> >(Um, now though you can also answer Goldbach's >> Conjecture, and figure >> >out it's false. But unlikely to ever be >> demonstrated false with an >> >actual counterexample which is sort of a depressing >> answer I guess.) >> > >> >So how could academic mathematicians take themselves >> seriously when >> >they ignore simple answers? >> > >> >I think it's because of the money. If math is your >> job and not just >> >a >> >hobby like for me, then simple answers can take away >> your paycheck. >> >And with that paycheck supporting you and maybe a >> family with a >> >mortgage, you care more about the paycheck than you >> do about >> >mathematics. >> > >> >So it's simple there as well: people paid to do >> mathematics often >> >cannot be trusted to tell the truth about >> mathematics if it impacts >> >their paycheck. >> > >> >I've seen that paid mathematicians routinely lie >> about mathematics. >> >Routinely lie. As in, it's quite normal for them to >> make things up >> >completely or avoid simple answers as simple answers >> don't pay the >> >bills! >> > >> >And you learn so much just from pondering twin >> primes and a simple >> >idea. >> > >> > >> >James Harris >>
From: David C. Ullrich on 2 Feb 2010 06:35 On Mon, 01 Feb 2010 22:42:26 -0800, Michael Press <rubrum(a)pacbell.net> wrote: >In article ><25332002-03c1-48bd-b48d-d641aa5e7871(a)m24g2000prn.googlegroups.com>, > JSH <jstevh(a)gmail.com> wrote: > >> I can prove but mathematicians believe they have the right to only >> care about something if it personally interests them--and doesn't >> impact their career! > >`Impact' is not a verb. Usually your prose writing >skills are better than this. Erm. Before posting spelling/grammar/usage flames you should make certain to get your facts straight. "Impact" certainly is a verb (as well as a noun, of course).
From: David C. Ullrich on 2 Feb 2010 06:37 On Mon, 1 Feb 2010 17:16:58 -0800 (PST), JSH <jstevh(a)gmail.com> wrote: >On Feb 1, 5:02�pm, William Hughes <wpihug...(a)hotmail.com> wrote: >> On Feb 1, 8:51�pm, JSH <jst...(a)gmail.com> wrote: >> >> > The twin primes probability result is such an overwhelming one as >> > mathematicians have been working for years building up data in support >> > of it. >> >> The GC result is such an overwhelming one as >> mathematicians have been working for years building up data in support >> of it. > >Except the prime residue axiom leads to a proof that Goldbach's >Conjecture is false. > >So there is a refutation by mathematical proof. Giggle. Right. Of course Ullrich's Axiom, which states that GC is false, leads to a much simpler proof that GC is false. How convenient - didn't realize we got to just invent our own axioms and use them as needed. > >> Therefore GC is true. >> >> � � � � � � � � � � � � � �- William Hughes > >Wrong. Goldbach's Conjecture is false. Sorry. > >Everything goes back to the prime residue axiom. > >The proof of the twin primes theorem relies on the prime residue >axiom. > >That axiom is supported by YEARS of data carefully gathered by >mathematicians researching prime numbers. > >Curious readers can find the equation that results from the prime >residue axiom in current literature: > >((p_j - 2)/(p_j -1))*((p_{j-1} - 2)/(p_{j-1} - 1))*...*(1/2) > >The HUGE gotcha in this thing is the irony of full support from >established research and it reveals why it's so hard in a situation >when there are people who hate the truth. > >Real math students would find the support wonderful and amazing. >After all, what's true is true. > >Fighting it is like getting mad because the earth isn't the center of >the universe or isn't flat. > >But as readers see the fight I want them to pay attention to it. > >If math people can ignore this result then they get continued FUNDING >in an area where their own research shows that continued investigation >is a waste of time. > >And the world goes without most knowing that random is about prime >preference--or lack of it. > >Freaking prime numbers may be the reason for random in our physical >world. > >Wow. > > >James Harris
From: Aatu Koskensilta on 2 Feb 2010 07:13 David C. Ullrich <ullrich(a)math.okstate.edu> writes: > Of course Ullrich's Axiom, which states that GC is false, leads to a > much simpler proof that GC is false. But is your axiom an "overwhelming one as mathematicians have been working for years building up data in support of it"? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: David R Tribble on 2 Feb 2010 17:05
JSH wrote: >> Except the [my] prime residue axiom leads to a proof that Goldbach's >> Conjecture is false. >> So there is a refutation by mathematical proof > David C. Ullrich writes: >> Of course Ullrich's Axiom, which states that GC is false, leads to a >> much simpler proof that GC is false. > Aatu Koskensilta wrote: > But is your axiom an "overwhelming one as mathematicians have been > working for years building up data in support of it"? Well, anyone can extend the usual system by adding his own axioms, consistent or not. It's just that what you get then is not the usual system anymore. So JSH's axiom, even if it were actually comprehensible, does not solve anything in standard mathematics. Most of the posters here understand this. Obviously, JSH does not. |