JSH: Twin primes
in [Math]
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From: JSH on 2 Feb 2010 19:55 On Feb 1, 2:21 pm, master1729 <tommy1...(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 > > notice about the range 13^2 - 17^2 that if we sum the probabilities of the previous ranges : > > 2.5 + 2.25 + 4.69 + 2.53 + 5.67 = 17.64 > > 17.64 is about the sum of actual values : 17 !! > > intresting ! Yes, it is. You're looking at what random looks like. Primes held the secret all along--with their behavior relative to each other by residue. Kind of weird to finally know for sure that you're looking at a random distribution, and seeing how it behaves. James Harris
From: Michael Press on 2 Feb 2010 22:59 In article <87hbq0dt9r.fsf(a)dialatheia.truth.invalid>, Aatu Koskensilta <aatu.koskensilta(a)uta.fi> wrote: > Michael Press <rubrum(a)pacbell.net> writes: > > > 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. > > Yes it is. So it is. IMPACT'', v.t. [L. impactus, from impingo; in and pango, to drive.] To drive close; to press or drive firmly together. -- Michael Press
From: Michael Press on 2 Feb 2010 23:00 In article <1d3gm5tfvqhvg23e22eo6eqjav7ealbf36(a)4ax.com>, David C. Ullrich <ullrich(a)math.okstate.edu> wrote: > 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). Yes, I should. Even do it sometimes. Thanks. -- Michael Press
From: JSH on 2 Feb 2010 23:21 On Feb 1, 5:32 pm, William Hughes <wpihug...(a)hotmail.com> wrote: > On Feb 1, 9:16 pm, JSH <jst...(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. > > Wooosh! > > The point is that both the GC and the "prime residue axiom" > are supported by lots of numerical evidence. > Why do you conclude that one is true and the other false? > > - William Hughes It is self-evident that primes do not have a residue preference. For instance, why would 3 wish for primes to have 1 as a residue versus 2? I use "wish" deliberately to ask for intent. If there is no intent, then by what mechanism could such a preference result? That is what makes an axiom--self-evidence. In contrast Goldbach's Conjecture is not self-evident. It does not require intent to ask if every composite can be written as the product of 2 primes. But worse, with the prime residue axiom that is self-evident, you can disprove Goldbach's Conjecture. I notice that no one has asked how. Wow. Can you believe that? Not a single question as to how. Even as a mental exercise, one would think that some of you would be curious about how you disprove Goldbach's Conjecture with something as simple as saying that primes have no residue preference. But curiosity requires humanity. James Harris
From: Marshall on 2 Feb 2010 23:35
On Feb 2, 8:21 pm, JSH <jst...(a)gmail.com> wrote: > > It is self-evident that primes do not have a residue preference. Primes prefer not to be anthropomorphized. It makes them angry. They like to think they're better than humans. Marshall |