# 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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### On the connection between $\pi(x)-Li(x)$ and $\theta(x)-x$

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### Convergence with the recurrence $T_{n+1}=T_n^2-T_n+\frac{n}{p_n}$

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### Prime numbers and sieving up to $q(x)=\log(x)(1+o(1))$

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### Complexity of representations of sets using elementary functions

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### From Firoozbakht's conjecture to set interesting conjectures for sequences or series of primes

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### On values of $n\geq 1$ satisfying that for all primorial $N_k$ less than $n$ the difference $n-N_k$ is a prime number

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### Is the ratio of a number to the variance of its divisors injective?

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### On the integral $I_s = \int_{1}^{\infty} (\pi(x)-Li(x))x^{-s-1} \mathrm{d}x$-follow up question

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### On the integral $I_s =\int_{1}^{\infty} (\pi(x)-Li(x))x^{-s-1} dx$

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### Is it possible to get a conjecture similar to Mandl's conjecture for a different arithmetic function of number theory, mainly related to primes?

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### On the product $\prod_{k=1}^{(p-1)/2}(x-e^{2\pi i k^2/p})$ with $x$ a root of unity

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### Is there a Kolmogorov complexity proof of the prime number theorem?

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### What about series involving strong primes?

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### A conjectural formula for the class number of the field $\mathbb Q(\sqrt{-p})$ with $p\equiv3\pmod8$

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