daniel
Reputation
4,615
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
 Feb6 awarded Benefactor Feb6 comment Minimal distance limit problem Am awarding bounty lest I forget and it expire and because I think this is right. When I have worked through it carefully I will accept the answer, but at least there's no expiration date there. Much appreciated. Feb6 comment Is an upper bound known for the least exponent $k$ such that $(\pi(n^k)-\pi(n))_{n=1}^\infty$ is strictly increasing? Feb6 comment Is an upper bound known for the least exponent $k$ such that $(\pi(n^k)-\pi(n))_{n=1}^\infty$ is strictly increasing? Do you have a cite for "I think the k=3 variant...?" Feb6 revised Minimal distance limit problem added 1 character in body Feb6 comment Primes of form $x^2+x\pm k$ Please don't upvote--was just fixing a problem with notation. Thanks. Feb6 revised Primes of form $x^2+x\pm k$ fixed notation. Feb5 comment Minimal distance limit problem My suggestion is that you reduce this to a comment until you can make it clearer. The ideas mentioned by Sary and G. Lowther in comments are IMO the sort of thing that could work. Apart from the lack of linguistic clarity in your proposed answer I am not sure you have broached an idea that will prove the conjecture. Feb5 comment Minimal distance limit problem @GeorgeLowther: Look forward to seeing it. Will look at the links when I have a chance. Feb3 comment Bounds on a sum involving the Möbius function It's also the error estimate de la Vallee Poussin found in his original proof of the PNT. Harold Edwards, Riemann's Zeta Function, p.82. Feb2 comment Bounds on a sum involving the Möbius function The link in this post is dead. A proper reference for both M(x) and A(x) is given in G.J.O. Jameson's The Prime Number Theorem, Thm. 5.1.9. page 186 (2003). An earlier source for M(x) is Landau's Handbuch vol.II, sec. 164, page 613 (1909) (the proof is in preceding pages). Feb2 awarded Nice Question Feb2 comment Is the Wikipedia article on the proof for Bertrand's Postulate correct? @RobertSoupe: I was thinking the same thing. It's nice to have a solid reference, which the $4^n$ version was. Feb1 comment Is the Wikipedia article on the proof for Bertrand's Postulate correct? I don't see how the proof works with $p\#_{p\leq n}<2^{2n-3},$ which is what their definition of $p\#$ implies. By proving $n = 2m-1$ you are only showing that $P(n)\implies P(n).$ Erdos uses \$p