# Questions tagged [prime-numbers]

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.

1,473 questions
Filter by
Sorted by
Tagged with
74 views

206 views

155 views

### A conditional approach to twin prime conjecture

Disclaimer: this question was first asked on a French forum (here comes the link for those of you who read French: http://www.les-mathematiques.net/phorum/read.php?5,1758830,1758922), but no ...
71 views

### Iteration of a primeness-measuring function

Question For $n \in \mathbb{N}$ let $\delta(n)$ denote the cardinality of the set $$\left\{(a,b) \in \mathbb{N}^2 \::\: 1 < a < n,\ 1 < b < n,\ n|ab\!\: \right\}.$$ Let $D(n)$ denote ...
166 views

### Explicit Formula for $n$th prime in terms of Riemann zeros?

We all know there exists a explicit Formula for prime counting function in terms of Riemann zeros. I'm wondering if similar formula exists for $n$th prime in terms of Riemann zeros?
126 views

### Is Brun's constant a period?

Brun proved that the sum of reciprocals of the twin primes is finite. This sum, Brun's constant, is not known to be irrational, (otherwise this would immediately entail the veracity of the twin prime ...
487 views

### Error term in Mertens' third theorem

Mertens' third theorem states that: $$\prod_{\substack{ p \leq x \\ \text{p prime} }} \left( 1 - \dfrac{1}{p} \right) \sim \dfrac{e^{-\gamma}}{\log(x)}$$ Question: what is the best functions (...
63 views

### Are numbers which are the product of n primes more common than numbers which are the product of n-1 primes? [duplicate]

In a recent video (https://www.facebook.com/188916357807416/videos/519169035700435/) Stephen Wolfram wonders whether, for every integer n>2, eventually the number of integers which are precisely the ...