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Apr
8
comment Unique factorization in $\mathbb Z(\sqrt{-19})$
Appreciate the late contribution. I will look at it as time allows. @mercio's answer did completely address my confusion, which was due to forgetting a definition.
Mar
19
comment Number of solutions of arithmetic funtion's equation.
Charles, thanks it's not necessary.
Mar
17
comment Inequality with prime numbers: $p_k+p_l+1\leq p_{k+l+1}$
Given your choice of notation it seems likely that Dusart's 1998 paper inspired the question. It seems worth citing. unilim.fr/laco/theses/1998/T1998_01.pdf
Mar
9
comment Legendre's Conjecture limit version
It seems likely to me that you meant $\lim \pi((n+1)^2)-\pi(n^2)$ for the question but you should edit to reflect this if true.
Feb
28
comment How to prove $\underset{p\leq n}{\prod}p^{\frac{1}{p-1}}\leq 2n$?
@Andrea: In the comment I mentioned that in principle we can show it for $n(1+\epsilon)$ for large enough $n$ and a clever technique. So yes, in principle. Also remember that as $\epsilon $ gets small you have an increasing burden for the finite $n< n_0$.
Feb
28
comment How to prove $\underset{p\leq n}{\prod}p^{\frac{1}{p-1}}\leq 2n$?
@Andrea: No not useless at all. In some sense the problem is solved. But there are a lot of proofs that go to great trouble to prove a particular case.
Feb
28
comment How to prove $\underset{p\leq n}{\prod}p^{\frac{1}{p-1}}\leq 2n$?
@Andrea: Almost. For example the prime number thm. gives that there is a prime on $(n,n(1+\epsilon))$ for any $\epsilon>0$ for suff. large $n.$ But to prove a particular $\epsilon $ may require ingenuity. So to make a claim you have to really have to take the extra step. And how big is $n?$
Feb
26
comment How to prove $\underset{p\leq n}{\prod}p^{\frac{1}{p-1}}\leq 2n$?
Also for any positive $\epsilon$ we have $\prod p^{1/(p-1)} \leq (1+\epsilon)n$ for sufficiently large n.
Feb
24
comment $k$-tuple conjecture.
I have edited my answer. It is more or less my earlier answer (and anon's) but you have simplified the question so I think this reflects the process up through Step 2 accurately.
Feb
21
comment $k$-tuple conjecture.
Deleted my answer, since I don't understand the question beyond the very basic example you gave. The gist of my answer was that I don't think your observations lead to new theorems about primes on short intervals, which is really just a comment.
Feb
18
comment $k$-tuple conjecture.
Let us continue this discussion in chat.
Feb
16
comment Curve profile for the logarithm-integral sum term of Riemann explicit formula?
@al-Hwarizmi: added a couple of lines in response to your comment. Continuing the process in the answer does not yield a closed form so I don't think there is much to be done with this. It's not a simple function.
Feb
13
comment Why does $\sum\limits_{k=1}^\infty \lfloor m/(n^k)\rfloor$ give you the number of times that $n$ divides $m!$?
@Andrea: You could make simplifications that I think would make the inequality true but they might depend on results that are also open questions. Even if you cannot prove the last inequality the question is a good model of a reasonable approach to something like this.
Feb
12
comment Why does $\sum\limits_{k=1}^\infty \lfloor m/(n^k)\rfloor$ give you the number of times that $n$ divides $m!$?
@Andrea: Your question about Legendre was well thought-out and IMO very good. I hope you will consider un-deleting. The inequality is difficult but I think it is true (maybe) and well worth thinking about. Sorry for the off-topic comment.
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
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
comment Primes of form $x^2+x\pm k$
Please don't upvote--was just fixing a problem with notation. Thanks.
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.