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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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Roth's theorem for primes in a given arithmetic progression to a large modulus
Let $\mathbb{P}_{a, q}$ denote the set of primes congruent to $a$ modulo $q$. Are there any estimates for the number of $3$-Arithmetic Progressions in the set $\mathbb{P}_{a, q}\cap [1, X]$, where $(a …