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Results tagged with prime-numbers
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user 18698
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.
1
vote
Accepted
On an attempt to create interesting variants of Firoozbakht's conjecture, evoking combinatio...
Yes, (2) holds for all large enough $n$.
According to Wikipedia (see also this question) $\frac{p_n}n=\log n+\log\log n-1+\frac{\log\log n}{\log n}(1+o(1))$, so
$$\frac{n+p_{n+1}}{n+1}=\log(n+1)+\log\ …
- 1,701
19
votes
Accepted
Prime plus square equals prime
Tao and Ziegler extended the Green-Tao theorem to the polynomial setting. As a very special case we get that any subset of the primes with positive relative density contains a difference which is a sq …
- 1,701
1
vote
0
answers
164
views
Are the Beatty primes asymptotically (Gowers) uniform?
A result of Green and Tao (initially conditional on two conjectures which were eventually settled by them and Ziegler) states that for any $s\in\mathbb N$,
$$\lim_{w\to\infty}\limsup_{N\to\infty}\sup_ …
- 1,701