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Definition

An arithmetic progression of primes is a set of primes of the form p_1 + k d for fixed p_1 and d and consecutive k, i.e., {p_1, p_1 + d, p_1 + 2d, ...}. For example, 199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089 is a 10-term arithmetic progression of primes with difference 210.