# Questions tagged [prime-gaps]

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### Related to one of the twin prime conjectures (In between squares)

This question is inspired by an answer that I have received for another question [see here]: One of the twin prime conjectures states that Between the squares of two consecutive odd numbers $[2n+1]^2$ ...
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### Comparing sets of twin primes with other sets. Why is there a max and min value?

I have taken 2 sets: The first is a consecutive list of the first prime of twin pairs. The second is a consecutive list of numbers as follow 1, 1+2, 1+2+3, 1+2+3+4, 1+2+3+4+5 .... I have then compared ...
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### Prime gap transform

Let $n$ be a large enough composite integer, and consider an arithmetic function $f$ that maps $n$ to the sum of prime gaps making a closed interval $J_{f}(n)$ containing $n$ whose extremities are ...
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### A generalization of strong primes

In this post we denote the sequence of prime numbers as $p_k$ for integers $k\geq 1$. I don't know if the following definition is in the literature. Definition. We define the $\theta$-strong primes, ...
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### On a conjecture about the arithmetic function that counts the number of twin primes

This is cross-posted from the question that I've asked with same title on Mathematics Stack Exchange two months ago, which has remained unanswered. Given a positive real number $x$ we will write ...
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### L. Gegenbauer's proof of Infinitude of Primes [closed]

I was going through the paper 'Euclid’S theorem on the infinitude of primes: A historical survey of its proofs' by Romeo Mestrovic where he mentioned that L. Gegenbauer proved Infinitude of Primes by ...
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### A Bonse's inequality for semiprimes, with a good mathematical content

A semiprime $s$ is a positive integer that is the product of two prime numbers, see Semiprine the encyclopedia Wikipedia. A well-known inequality, with applications, that involves prime numbers is the ...
538 views

### Can Scholze's perfectoid spaces bridge the gap for twin prime conjecture? [closed]

It seems than an analogue of the twin prime conjecture for polynomials in finite fields has been solved: see https://www.quantamagazine.org/big-question-about-primes-proved-in-small-number-systems-...
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### consecutive prime gaps and explicit bound

I am aware of the theorem that $p_{n+1}- p_n \leq n^{0.525}$ which is true for all sufficiently large numbers due to Baker, but if i want to make the implicit "for all sufficiently large numbers" ...
915 views

### $\pi((n+1)^2)-\pi(n^2) \le \pi(n)$ for all $n \ge 370$?

There are some conjectures of the form: There always exist at least $X$ prime numbers between $A$ and $B$. Examples: Bertrand's postulate: for every $n>1$ there is always at least one prime $p$ ...
The merit of a prime gap equals $(p_{n+1}-p_n)/\ln p_n$. One can interrogate the statistics of merit by first restricting $n<M$ for some $M$, and then letting $M$ approach $\infty$. The very ...