proof of hardy-littlewood 2nd conjecture
in [Math]
|
Prev: A Feasible Optimal Solution to the P Versus NP Problem: l=7
Next: Skew-symmetric matrix A and I + A - Cayley transform
From: Ludovicus on 6 May 2010 13:18 On May 6, 12:39 pm, A <anonymous.rubbert...(a)yahoo.com> wrote: > On May 6, 10:14 am, master1729 <tommy1...(a)gmail.com> wrote: > > each prime less than sqrt(b-a), this formula is wrong--there can be > more than that many primes in the interval (a,b). More? How? His formula say that Max.pi(a,b) = pi(0,b-a). This is 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
From: master1729 on 6 May 2010 11:43 luis A Rodriguez wrote : > On May 6, 12:39 pm, A > <anonymous.rubbert...(a)yahoo.com> wrote: > > On May 6, 10:14 am, master1729 > <tommy1...(a)gmail.com> wrote: > > > > > each prime less than sqrt(b-a), this formula is > wrong--there can be > > more than that many primes in the interval (a,b). > > More? How? > His formula say that Max.pi(a,b) = pi(0,b-a). not = , <=. consistant with what you wrote below. This > is 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 > tommy1729
From: master1729 on 6 May 2010 12:03 anonymous.rubbertube wrote : > On May 6, 10:14 am, master1729 <tommy1...(a)gmail.com> > wrote: > > no response. > > > > surely you must understand parts of it ?? > > > > I just looked over your "proof." It looks as though > you have > overlooked that any number which is the product of > more than one prime > will be sieved more than once. This means your > formula for the maximum > number of primes in the interval (a,b), which you > obtain by taking b-a > and subtracting 1 for each number sieved from the > interval (a,b) for > each prime less than sqrt(b-a), this formula is > wrong--there can be > more than that many primes in the interval (a,b). my proof gave C or C - 1. C does not mean floor(x/p). C and C - 1 are to illustrate that a prime sieves an interval of certain length a potential amount of times which differs by 1 , C or C - 1. we then sum the worst case difference of 1 and get pi(sqrt(c)) if you think this affects the equation strongly you are wrong. we get another correction which cancels itself out. let me clarify with an example. interval length 100. 3 sieves it 33 or 34 times. ( "or 1)" ) 5 sieves it 20 times. multiples of 15 are sieved by 3 and 5. but the number of times a multiple of 15 or equivalently a sieve of both 3 and 5 occurs is not independant or random !. 15 sieves it 6 or 7 times. ( "or 2)" ) note that "or 2" and "or 1" depend on eachother rather than being independant or random. and therefore it is already accounted for by "or 1" , which i used in my proof. regards tommy1729
From: christian.bau on 6 May 2010 17:30 On May 6, 3:14 pm, master1729 <tommy1...(a)gmail.com> wrote: > consider the closed interval (a,b). If you mean a closed interval, why don't you write [a, b]? Do you know the difference between (a, b), [a, b), (a, b] and [a, b] ?
From: christian.bau on 6 May 2010 17:35
On May 5, 11:42 pm, master1729 <tommy1...(a)gmail.com> wrote: > consider the closed interval (a,b). > > we need to prove that the number of primes in that > interval cannot be larger than pi(b - a). Wrong. We don't need to prove this. We only need to prove that the number of primes in the left open, right closed interval (a, b] cannot be larger than pi (b - a). If a and b are both primes, and the number of primes in [a, b] is one larger than the pi (b - a), then the conjecture could still be true. I'll leave you to it until you fix this, then I'll look for your next mistake. |