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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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Reference request: Numbers composed of given primes

The number of $n \leq x$ composed using only the given primes $p_1, p_2, ... p_k$ as $x \rightarrow \infty$ satisfies $$ \frac {\log^k x} {k! \prod_1^k p_j} + O \left ( \log^{k-1} x \right ) . $$ I am …