# Questions tagged [prime-gaps]

The tag has no usage guidance.

70 questions
Filter by
Sorted by
Tagged with
209 views

### Prime gaps that are "relatively" bigger than all later prime gaps: Is this in OEIS?

This OEIS entry is about Primes (lower end) with record gaps to the next consecutive prime: primes p(k) where p(k+1) - p(k) exceeds p(j+1) - p(j) for all j < k. I'm wondering about a different ...
• 11.4k
227 views

### The number of continuously increasing primes gaps in the interval $[2,n]$ is less than $\log n$

A prime gap is the difference between two successive prime numbers. The $n$-th prime gap, denoted gn or $g(p_n)$ is the difference between the $(n+1)$-st and the $n$-th prime numbers. Using my ...
• 1,076
1 vote
311 views

### On the number of primes between prime $p_n$ and $p_{n}^2$

does anyone knows if there are studies on the number of primes between prime $p_n$ and $p_{n}^2$, where $p_n$ is the $n$-th prime? I am studying it through the following formula: \begin{align} \pi(p^...
214 views

• 501
66 views

### Divisor of given order in short intervals

Is the following Open question or Conjecture already known, or eventually settled ? Open question : For sufficiently large $x$ there is at least a positive integer in the interval $[x,x+\log^2(x)]$ ...
• 378
420 views

### Primitive sequences with elements in every interval $[x, x + \sqrt x)$

We believe there is always a prime in the interval $[x,x+\sqrt{x})$, for $x$ sufficiently large, but proving this is inaccessible, even under RH. What if we just wanted a sequence of integers free of ...
1 vote
172 views

### Infinitely many $k \in \mathbb{N}$ such that the closed interval $[k, k+99]$ contains from $2$ to $23$ prime numbers

Let $k \in \mathbb{Z}^+$. Is it possible to prove that, for some given $m \in \{0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23\}$, there are only finitely many $k$ such that the closed ...
• 807
1 vote
3k views

### Contribution of Yitang Zhang latest results if correct to correlation conjecture of H. L. Montgomery?

There are some integrals related to the celebrated pair correlation conjecture of H. L. Montgomery. One of them is the integral introduced by Selberg related to estimating the variance of primes in ...
• 2,236
425 views

### What consequences would follow from the density hypothesis?

Let $N(\sigma,T)$ denote the number of zeros $\rho=\beta+\gamma i$ of the Riemann zeta function satisfying $\beta\ge \sigma$ and $0<\gamma\le T$, counted with multiplicity. Then the "Density ...
• 405