# 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.

**0**

**1**answer

### Analytic continuation and convergence of a Riemann zeta related function

**9**

**1**answer

### Possible contemporary improvement to bounded gaps between primes?

**1**

**0**answers

### Do $k$ specific prime factors uniquely determine the continuous composite sequence of length $k$?

**0**

**0**answers

### k specific prime factors guess and related prime guess [duplicate]

**0**

**0**answers

### On complexity of a particular prime problem

**1**

**1**answer

### Cyclotomic Numbers, Difference Sets

**2**

**1**answer

### A family of difference sets (paper by A. L. Whiteman)

**-6**

**0**answers

### Sieve methods and primal height

**10**

**1**answer

### Normal numbers, Liouville function, and the Riemann Hypothesis

**2**

**0**answers

### On the connection between sums of prime numbers and distribution of prime numbers

**2**

**1**answer

### Truncated Euler products, Dirichlet eta function, and convergence issues

**3**

**1**answer

### Formulas for $\sum_{x=1}^{n}\Big\{\frac{x^q}{n}\Big\}$

**-1**

**0**answers

### Gap repeating integers

**-1**

**1**answer

### A question on assigning finite values to divergent sums involving expression of primes

**-1**

**0**answers

### Does one have $\alpha_{n}\ll\sum_{p^m\leq n, m\geq 2}\Lambda(p^{m})\log n$?

**5**

**1**answer

### Weak Goldbach conjecture with distinct primes for odd integers between $4\times 10^{18}$ and $10^{27}$

**1**

**2**answers

### Twin Primes- Clement conjecture proof

**1**

**1**answer

### What is a non-trivial upper bound on the $k$th prime below a given prime $p$?

**0**

**0**answers

### Integers having the same digits as their prime factors

**-2**

**1**answer

### Divisors of numbers [closed]

**-1**

**0**answers

### Primality radius and Chebyshev's bias

**1**

**0**answers

### Approximating real numbers [closed]

**4**

**1**answer

### Is $\prod_{k=1}^nk^{\sigma(k)}$ a square or a cube for some $\sigma\in S_n$?

**2**

**0**answers

### Primes of the form $\frac{n^2-n+4}{2}$ satisfy Hardy-Littlewood analogue?

**1**

**0**answers

### Smooth number pairs satisfying a congruence

**4**

**1**answer

### The Diophantine equation $ (xz+1)(yz+1)=az^{3}+1$ has no solutions in positive integers with $z > a^2+2a$

**0**

**0**answers

### Primality of $n$ bit integers in depth $n^\alpha$ under standard conjectures?

**9**

**0**answers

### Is $\pi (x)=\operatorname{R}(x)-\sum_{\rho}\operatorname{R}(x^{\rho})$ correct at all?

**0**

**0**answers

### Are there infinitely many solution $(a,b,p)$ satisfying $a^b+b^a=p$?

**0**

**1**answer

### Upper bound for the number of $k$-central numbers in a prime gap

**-1**

**1**answer

### Prove using Dyck naturals: for $n \in \mathbb{N}_{+}$ and big enough $k \in \mathbb{N}_{+}$, $p_{k-1} < \cdots < np_{k-a_{n}}$ (a is A073093)

**13**

**2**answers

### information-theoretic derivation of the prime number theorem

**21**

**1**answer

### How to see that the determinant of this matrix is nonzero for all primes?

**2**

**0**answers

### On a result of Euler on pseudoprimes

**0**

**0**answers

### $f$ - arithmetic functions

**6**

**1**answer

### Set of prime numbers $q$ such that $\sum\limits_{p\leq\sqrt{q}}p=\pi(q)$, where $p$ are prime numbers

**0**

**0**answers

### Primes in many variables polynomials form

**5**

**0**answers

### Small multiplicative order modulo infinitely many primes

**4**

**0**answers

### On $\sum_{n=1}^\infty\frac1{p_1+\cdots+p_n}$ and $\sum_{n=1}^\infty\frac1{p_1\cdots p_n}$

**5**

**1**answer

### Quadratic Diophantine equations with all values prime

**0**

**0**answers

### Gaussian primality radius

**1**

**1**answer

### Comparing densities of different gapped primes (twin, cousin, sexy…) [closed]

**1**

**0**answers

### Numbers whose digits, in order, display prime factors

**15**

**2**answers

### Is the surreal number $\omega(\sqrt{2}+1)+1$ a prime?

**8**

**6**answers

### How many solutions are there to the equation $x^2 + 3y^2 \equiv 1 \pmod{p}$?

**0**

**1**answer

### How differently would we model the distribution of primes if prime gap is larger?

**0**

**0**answers

### On a generalised result of Mertens

**50**

**5**answers

### What is the simplest proof that the density of primes goes to zero?

**0**

**1**answer

### What are the complexity classes of these problems about divisibility and coprimality?

**4**

**0**answers