The title refers to the fact, noted by Chebyshev in 1853, that
primes congruent to 3 modulo 4 seem to predominate over those congruent to 1.
We study this phenomenon and its generalizations. Assuming the Generalized Riemann
Hypothesis and the Grand Simplicity Hypothesis (about the zeros of the
\hbox{Dirichlet} $L$-function), we can characterize exactly those moduli and
residue classes for which the bias is present. We also give results
of numerical investigations on the prevalence of the bias for several
moduli. Finally, we briefly discuss generalizations of the bias to
the distribution to primes in ideal classes in number fields, and to
prime geodesics in homology classes on hyperbolic surfaces.