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Feb
9
comment Proving that there are at least $n$ primes between $n$ and $n^2$ for $n \ge 6$
Isn't this maybe also a consequence of known error bounds for $\pi(x)\sim x/log (x)?$
Feb
6
awarded  Benefactor
Feb
6
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.
Feb
6
comment Is an upper bound known for the least exponent $k$ such that $(\pi(n^k)-\pi(n))_{n=1}^\infty$ is strictly increasing?
Also, math.stackexchange.com/questions/142535/…
Feb
6
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...?"
Feb
6
revised Minimal distance limit problem
added 1 character in body
Feb
6
comment Primes of form $x^2+x\pm k$
Please don't upvote--was just fixing a problem with notation. Thanks.
Feb
6
revised Primes of form $x^2+x\pm k$
fixed notation.
Feb
5
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.
Feb
5
comment Minimal distance limit problem
@GeorgeLowther: Look forward to seeing it. Will look at the links when I have a chance.
Feb
3
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.
Feb
2
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).
Feb
2
awarded  Nice Question
Feb
2
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.
Feb
1
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 $p<n$ and shows this implies $p=n+1.$
Feb
1
comment Is the Wikipedia article on the proof for Bertrand's Postulate correct?
Here is a link to Erdos' article. renyi.hu/~p_erdos/1989-29.pdf. The discussion is in the first couple of pages. His proof in form is pretty much that of the Wiki article. In Erdos' proof by assuming $p<n$ he shows $\geq n+1.$ That is the induction.
Feb
1
comment Is the Wikipedia article on the proof for Bertrand's Postulate correct?
I think $2^{2(2m-3)}$ should be $2^{2(2m)-3}.$ Just a typo in the article.
Jan
31
revised Minimal distance limit problem
added 75 characters in body
Jan
29
comment Numbers that are divisible by the number of primes smaller than them
On second thought there is no obligation on your part, so I will just mention here that the question (and the proof below) were noted in another question mathoverflow.net/questions/139934/….
Jan
29
comment Numbers that are divisible by the number of primes smaller than them
This was in AMM vol. 69. no.1 1962. It might be good to include the full cite in case someone wants to look it up.+1 for the information.