proof of hardy-littlewood 2nd conjecture
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From: jbriggs444 on 4 May 2010 12:24 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? Without any further conditions?
From: master1729 on 4 May 2010 08:50 > 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? > > Without any further conditions? google hardy-littlewood first before posting here. say after me : google is my friend. oh what the **** http://mathworld.wolfram.com/Hardy-LittlewoodConjectures.html notice a and b ( or x and y resp ) need to be >=2. tommy1729
From: jbriggs444 on 4 May 2010 13:24 On May 4, 12:50 pm, master1729 <tommy1...(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? > > > Without any further conditions? > > google hardy-littlewood first before posting here. > > say after me : google is my friend. > > oh what the **** > > http://mathworld.wolfram.com/Hardy-LittlewoodConjectures.html > > notice a and b ( or x and y resp ) need to be >=2. > > tommy1729- Hide quoted text - > > - Show quoted text I did google it first. To the extent that your attempted proof fails to use that clause, it is subject to counter-example. Not counter-examples to the conjecture. Counter-examples to the proof.
From: christian.bau on 4 May 2010 16:31 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: christian.bau on 4 May 2010 16:35
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-LittlewoodConjectures.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. |