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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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Counting smooth numbers in short intervals

Suppose that $F(s) = \sum_{n \sim x} a_n n^{-s}$ where $a_n = 1$ if $n$ is $x^{\varepsilon}$ smooth and $a_n = 0$ otherwise. We want to understand the distribution of the $a_n$'s in a short interval o …
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