# 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.

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### What is easier to find, the next prime number or next zero of zeta function?

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### How to choose a prime p s.t. n-th cyclotomic polynomial splits into as much as possible irreducible polynomials while p is almost constant size?

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### Perfect Runs of Consecutive Integers

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### Robin's inequality and the zeros of the Riemann zeta function

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### Weak k-Tuple conjecture form and what we should prove [closed]

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### Why shouldn't this prove the Prime Number Theorem?

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### What was the first elementary proof that $\pi(x)=o(x)$?

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### on generating prime numbers [closed]

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### Estimating integral of product of terms $\cos(t\log p)$

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### Reversing the CRT: Is $5$ tough?

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### Order of magnitude of $\sum \frac{1}{\log^2{p}}$, or $\sum \frac{1}{\log^a{p}}$ for arbitrary power $a$ [closed]

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### Covering the primes with pairs of consecutive integers

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### Does the average primeness of natural numbers tend to zero?

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### Decoding non-trivial zeros of the Riemann zeta function from prime numbers

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