Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with prime-numbers
Search options not deleted
user 13625
Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.
0
votes
1
answer
236
views
Is it consistent with Cramer's conjecture to conjecture that $x/\pi_{2}(x)>2B_{2}/6\times\lo...
Brun's constant $B_{2}$ is defined as $B_{2}=1/3+1/5+1/5+1/7+1/11+1/13+...$ where the sum is taken on $p$ such that $p$ is an element of a couple of twin primes. The number of twin primes below is exp …
- 6,974
0
votes
1
answer
250
views
Asymptotics for a peculiar kind of squarefree numbers
Let $ n $ denote a square free positive composite integer, $ \omega(n) $ its number of prime factors, $ P_{i}(n) $ its $ i $ -th prime factor.
Can we determine an asymptotics for the number of …
- 6,974
2
votes
1
answer
972
views
About Extended Goldbach's conjecture
Hello,
This question is a follow-up from About Goldbach's conjecture.
As $N_{2}(n)=\sum_{r\leq n}1_{\mathbb{P}}(n-r)1_{\mathbb{P}}(n+r)$, Chebotarev's theorem allows to write:
$$\dfrac{N_{2}(n)}{ …
- 6,974
2
votes
Is $\Bigl\{ n \sum_{k=2}^{n-1} \frac{1}{k}\Bigr\}$ unique $\forall n \in \Bbb{N}, n>1$
Only a partial answer for now, as it is too long for a comment. From my comment and Carlo Beenakker's answer, it suffices to consider the case where $n$ and $m$ have different radicals but the same pa …
- 6,974
6
votes
Constant $a$ such that $[a^n]$ is always prime for $n\in N^+$
Maybe not exactly what you're looking for, but in his book "Merveilleux nombres premiers" (in French), Jean-Paul Delahaye mentions the so-called Mills' constant $A=1.30637788386...$ which fulfills, un …
- 6,974
4
votes
2
answers
970
views
Lower bound for a prime gap occurring infinitely often
In his striking paper of may 2013, Zhang showed the existence of an even integer $g\lt 70,000,000$ such that $g$ is a prime gap occurring infinitely often. What is the best unconditional lower bound f …
- 6,974
6
votes
0
answers
726
views
Would the following conjectures imply Cramer's conjecture?
Assume Goldbach's conjecture. Then for every $n\ge 2$ there exists at least one non-negative integer $r\le n-2$ such that both $n+r$ and $n-r$ are primes. Let's write $r_{0}(n):=\inf\{r\le n-2, (n-r,n …
- 6,974
5
votes
1
answer
618
views
Has this strengthening of the PNT already been conjectured?
Suppose $f:\mathbb{Z}_{\geq 0}\to\mathbb{Z}_{\geq 0}$ is an arithmetic function that grows slower than the identity map. Has it already been conjectured that, under this general hypotheses, $\pi(n+f(n …
- 6,974
6
votes
1
answer
725
views
is there any heuristics suggesting that the number of Fibonacci primes below $x$ is equivale...
The question of knowing whether there are infinitely many Fibonacci primes is an open question. As $F_p$ is prime only if $p$ is prime, one has $\pi_{FP}(x)\le \pi(\log_{\phi} x+0.5\log 5)$, but numer …
- 6,974
11
votes
0
answers
2k
views
Would the following conjectures imply $\lim\inf_{n\to\infty}p_{n+k}-p_{n}=O(k\log k)$?
Assume Goldbach's conjecture. Then for every $n\ge 2$ there exists at least one non-negative integer $r\le n-2$ such that both $n+r$ and $n-r$ are primes. Let's write $r_{0}(n):=\inf\{r\le n-2, (n-r,n …
- 6,974
-8
votes
1
answer
383
views
Is $2^{p}-1$ prime iff for $\frac{p-1}{2}$ odd positive integers $n$ below $p$, $(n+2)\vert ... [closed]
As I was playing around with Mersenne numbers, and discovered the notion of Wagstaff prime going off Wikipedia, I started considering the sequence, for a given $odd$ prime number $p$, defined as follo …
- 6,974
5
votes
1
answer
658
views
Does $0<k<n$ imply $p_{n+k}<\left(1+\frac{1}{k}\right)^k p_{n}$ for large enough $n$?
Disclaimer: a stronger version of this question was first asked on MSE: https://math.stackexchange.com/questions/3896547/does-p-nk1-frac1kk-p-n-whenever-0kn/3896842#3896842 and on a French math forum …
- 6,974
0
votes
0
answers
142
views
Expliciting the distance between consecutive Goldbach numbers assuming it's finite
In this paper, the author shows unconditionally that at least one of the following statements holds:
i) the distance between two consecutive Goldbach numbers is finite, i.e. there exists an absolut …
- 6,974
0
votes
0
answers
140
views
Bounding $\dfrac{r(x)}{\pi(x+r(x))-\pi(x-r(x))}$ with $1\ll r(x)\ll \log^{4}(x)$
I would like to know whether it is possible to obtain the bounds $\sqrt{r(x)}\ll k(x)\ll r(x)$ where $k(x)={\pi(x+r(x))-\pi(x-r(x))}$ and $1\ll r(x)\ll \log^{4}(x)$ and thus $1\ll\dfrac{r(x)}{\pi(x+r( …
- 6,974
2
votes
1
answer
186
views
Integers whose product is a primorial and primality of their sum or difference
Let $ a $ and $ b $ be two positive integers such that $ a\lt b $ and $ ab $ is a primorial. Let $\mathcal{N}(x)=\mathcal{N}_{prime}(x)+\mathcal{N}_{pure}(x)+\mathcal{N}_{mixed}(x)$ where $ \m …
- 6,974