Does the universe favor prime numbers?

Determine whether the universe favors prime numbers by testing if the number of member galaxies in galaxy groups or clusters exhibits a statistical preference for prime values over composite values, relative to expectations from the prime number distribution (e.g., approximated by Riemann’s R(x)).

Background

Motivated by reports that large-scale cosmological data may exhibit parity-odd preferences, the paper asks whether a similar preference exists for prime numbers. To operationalize this question, the authors analyze galaxy group catalogs (DESI Legacy Imaging Surveys DR9) and compare the observed fraction of groups with prime-sized membership to theoretical expectations from prime number statistics.

The study frames the problem as a statistical test of whether group membership counts are disproportionately prime, using Riemann’s R(x) as a reference for expected prime fractions across specified membership ranges.