# Residue classes containing an unexpected number of primes Article - Décembre 2012

Daniel Fiorilli

Daniel Fiorilli, « Residue classes containing an unexpected number of primes  », Duke Mathematical Journal, décembre 2012, pp. 2923-2943. ISSN 0012-7094

Abstract

We fix a non-zero integer \$a\$ and consider arithmetic progressions \$a \bmod q\$, with \$q\$ varying over a given range. We show that for certain specific values of \$a\$, the arithmetic progressions \$a \bmod q\$ contain, on average, significantly fewer primes than expected.