proof of hardy-littlewood 2nd conjecture
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From: christian.bau on 4 May 2010 16:35 On May 4, 5:24 pm, jbriggs444 <jbriggs...(a)gmail.com> wrote: > On May 4, 10:51 am, master1729 <tommy1...(a)gmail.com> wrote: > > > > > > > gnasher729 wrote : > > > > On May 1, 10:19 pm, master1729 <tommy1...(a)gmail.com> > > > wrote: > > > > proof of hardy-littlewood 2nd conjecture. > > > > > consider the interval (a,b). > > > > > we need to prove that the number of primes in that > > > interval cannot be larger than pi(b - a). > > > > > thus pi(a,b) <= pi(b - a). > > > > Please post your proof again after adding a > > > definition of pi (a, b). > > > pi(a,b) is the number of primes in the interval (a,b). > > So, for instance, pi(17,17) = 1 and pi(0) = 0? > And you need to prove that the former is smaller than the latter? (17, 17) is an empty set. With the definition above, pi (17 17) = 0.
From: master1729 on 4 May 2010 12:47 > On May 4, 5:50 pm, master1729 <tommy1...(a)gmail.com> > wrote: > > > say after me : google is my friend. > > > > oh what the **** > > > > > http://mathworld.wolfram.com/Hardy-LittlewoodConjectur > es.html > > > > notice a and b ( or x and y resp ) need to be >=2. > > > > tommy1729 > > Now do you think we should have to put a proof > together in bits and > pieces? Please post a complete proof with nothing > missing. No stupid > mistakes like using an undefined pi (x, y), no stupid > mistakes like > claiming that there is a prime in the open interval > (17, 17). A > complete proof. We will then go and show you the next > mistake. But not > in something put together in bits and pieces. i did not talk about interval (17,17). pi(x,y) is the amount of primes between x and y. what part is not clear to you ?
From: master1729 on 4 May 2010 13:29 Re: proof of hardy-littlewood 2nd conjecture ******************************************** im willing to clarify particular confusions , just show me where you are confused/i am unclear. the proof is complete , not formal , but at least complete. it might be counterintuitive and confusing to some/many. pi(a,b) is the amount of primes between a and b. ( though not defined by me this is commenly seen in paper concerning prime counting functions and related ) it is not 'statistical' it is 'combinatorial' and thus with certainty. no probabilities. it might be helpfull to try to understand that pi(a,b) <= pi(b - a) + 2 follows easily from my proof. im waiting for more people to comment. that might help the dialogue. regards the master tommy1729
From: christian.bau on 4 May 2010 17:47 On May 4, 9:47 pm, master1729 <tommy1...(a)gmail.com> wrote: > > On May 4, 5:50 pm, master1729 <tommy1...(a)gmail.com> > > wrote: > > > > say after me : google is my friend. > > > > oh what the **** > > >http://mathworld.wolfram.com/Hardy-LittlewoodConjectur > > es.html > > > > notice a and b ( or x and y resp ) need to be >=2. > > > > tommy1729 > > > Now do you think we should have to put a proof > > together in bits and > > pieces? Please post a complete proof with nothing > > missing. No stupid > > mistakes like using an undefined pi (x, y), no stupid > > mistakes like > > claiming that there is a prime in the open interval > > (17, 17). A > > complete proof. We will then go and show you the next > > mistake. But not > > in something put together in bits and pieces. > > i did not talk about interval (17,17). > > pi(x,y) is the amount of primes between x and y. > > what part is not clear to you ? 1. You mean the number of primes? Like in counting (13, 17, 19) = 3 primes. "Amount" of primes is not a term that has any defined mathematical meaning. You can't prove anything if you don't use terms that are clear. 2. The number of primes _between_ x and x+y is irrelevant; you need the number of primes from x+1 to x+y inclusive. That's one more prime if x+y is a prime. Waiting for a corrected _complete_ proof with everything inside it defined. Like for example: Let pi (x) be the number of primes p such that 1 <= p <= x. Let pi (x, y) be the number of primes p such that x < p <= y (or whatever definition you want, but for heaven's sake DEFINE IT.
From: Ludovicus on 4 May 2010 20:08
On May 1, 5:19 pm, master1729 <tommy1...(a)gmail.com> wrote: > proof of hardy-littlewood 2nd conjecture. > c = b - a > max pi(a,b) = pi(c) > tommy1729 That is utterly false. It was demonstrated that ever: pi(a, a+50) <= 14 but pi(50) = 15 The only known cases that pi(a,b) = pi(b-a) are pi(a, a+16) = pi(16) and pi(a + 36) = pi(36) Ludovicus |