Chromatic congruences and Bernoulli numbers

For every natural number n and a fixed prime p, we prove a new congruence for the orbifold Euler characteristic of a group. The p-adic limit of these congruences as n tends to infinity recovers the Brown-Quillen congruence. We apply these results to mapping class groups and using the Harer-Zagier formula we obtain a family of congruences for Bernoulli numbers. We show that these congruences in particular recover classical congruences for Bernoulli numbers due to Kummer, Voronoi, Carlitz, and Cohen.