Chebyshev's bias

From Pafnuty Chebyshev, the discoverer.

Chebyshev's bias

1. The phenomenon that most of the time, there are more prime numbers of the form 4k + 3 than of the form 4k + 1 up to n.
2. The phenomenon that if ${\displaystyle a}$ is a quadratic residue modulo ${\displaystyle q}$ and ${\displaystyle b}$ is a quadratic nonresidue modulo ${\displaystyle q}$, then ${\displaystyle \pi (x;b,q)>\pi (x;a,q)}$ occurs more often than not