Residue classes containing an unexpected number of primes
Daniel Fiorilli

TL;DR
This paper investigates specific residue classes modulo q that contain fewer primes than expected, revealing unexpected prime distribution patterns in arithmetic progressions for certain fixed residues.
Contribution
It demonstrates that for particular fixed residues, the distribution of primes in arithmetic progressions deviates significantly from the expected average.
Findings
Certain residue classes contain fewer primes than predicted
The deviation is significant for specific fixed residues
Results contribute to understanding prime distribution irregularities
Abstract
We fix a non-zero integer and consider arithmetic progressions , with varying over a given range. We show that for certain specific values of , the arithmetic progressions contain, on average, significantly fewer primes than expected.
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