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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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Are there infinitely many primes of the form $\lfloor e x\rfloor$ for $x\in\mathbb{Z}^+$?

Construct a function $f(x)=\lfloor e x\rfloor$. For each positive integer $x$, $f(x)$ will be a positive integer. Among these integers $f(x)$, are there an infinite number of primes?