Prime After Prime [Hayes] - Printable Version

In “Prime After Prime,” mathematician and science writer Brian Hayes explores a surprising discovery about prime numbers: although primes appear randomly distributed, consecutive primes exhibit strong and unexpected biases when grouped by their remainders modulo a number such as 3 or 7. Building on work by Robert J. Lemke Oliver and Kannan Soundararajan, Hayes shows that certain residue classes are significantly more or less likely to follow one another than pure randomness would suggest, revealing hidden structure in the sequence of primes.

Through computational experiments, visualizations, and discussion of analytic number theory, he examines how these patterns relate to prime gaps, congruence classes, and “jumping champions,” concluding that even one of mathematics’ most studied objects still contains remarkable and unexpected regularities.