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 2233
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.
44
votes
Accepted
For consecutive primes $a\lt b\lt c$, prove that $a+b\ge c$.
Yes, this is true. In 1952, Nagura proved that for $n \geq 25$, there is always a prime between $n$ and $\frac{6}{5} n$. Thus, let $p_k$ be a prime at least $25$. Then $p_k+p_{k+1} > 2p_k$. But by …
- 32.1k
7
votes
Are there five consecutive primes in arithmetic progression?
Yes. In fact, there is a set of 10 consecutive primes that are in arithmetic progression. I believe this is the longest known set. See here.
- 32.1k
3
votes
Bringing Number and Graph Theory Together: A Conjecture on Prime Numbers
I don't really know the answer, but I suppose I would first start by trying to disprove the conjecture. After all, it has only been verified for graphs up to order 5. The obvious counterexamples I w …
- 32.1k
4
votes
What are conjectures that are true for primes but then turned out to be false for some compo...
An important question in matroid structure theory is given a matroid $M$, how many inequivalent representations does it have over a fixed finite field $\mathbb{F}$? Two $\mathbb{F}$-matrices $A$ and …
- 32.1k
10
votes
Accepted
Is the factorization of $a_m-a_n$ affected by the fact that $\Sigma \frac{1}{a_k}<+\infty$?
No, this is false. Define $a_1=1$, and for all $k \geq 2$ let $a_k = \big\lfloor \frac{k}{2}\big\rfloor^2$. Note that $\sum_{k=1}^\infty \frac{1}{a_k}$ converges since it is equal to $1+2\sum_{k=1}^ …
- 32.1k
11
votes
Accepted
Which even numbers are known to be both prime gaps and the sum of 2 primes?
Goldbach's Conjecture has been verified for all numbers up to $4 \times 10^{18}$ by Oliveira e Silva, Herzog, Pardi. On the other hand, Thomas R. Nicely has shown that all even numbers up to $2000$ o …
- 32.1k