On the constant in the Mertens product for arithmetic progressions. II. Numerical values

TL;DR

This paper provides highly precise numerical values for the constant in the Mertens product over primes in various arithmetic progressions, enhancing the understanding of prime distribution in these sequences.

Contribution

It offers explicit numerical constants with 100 decimal digits for primes in arithmetic progressions with moduli up to 100, filling a gap in computational number theory.

Findings

Numerical constants computed with 100 decimal digits

Constants provided for all coprime residue classes modulo q (3 ≤ q ≤ 100)

Enhances precision in prime distribution studies

Abstract

We give explicit numerical values with 100 decimal digits for the constant in the Mertens product over primes in the arithmetic progressions $a \bmod q$, for $q \in \{3$, ..., $100\}$ and $(a, q) = 1$.