Let k be an integer ≥ 1 and let l be an integer such that 1 ≤ l ≤ k, (l,k) = 1. An asymptotic formula (valid for large x) is obtained for the product ∏ p≤x,p≡l(modk)1- 1 p, generalizing a familiar result of Mertens.

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Persistent URL dx.doi.org/10.1016/0022-314X(74)90032-8
Journal Journal of Number Theory
Williams, K.S. (1974). Merten's theorem for arithmetic progressions. Journal of Number Theory, 6(5), 353–359. doi:10.1016/0022-314X(74)90032-8