A prime number race compares the counts of primes in different reduced residue classes modulo an integer 
. Writing 
for the number of primes 
with 
, a race asks which of 
is largest as 
varies. Although the prime number theorem for arithmetic progressions
gives the same leading asymptotic for every reduced residue class, persistent finite-range
biases can occur, such as Chebyshev's bias between primes congruent to 3 and 1 modulo
4.
Prime Number Race
See also
Dirichlet's Theorem, Prime Number TheoremExplore with Wolfram|Alpha
References
Rubinstein, M. and Sarnak, P. "Chebyshev's Bias." Experiment. Math. 3, 173-197, 1994.Cite this as:
Weisstein, Eric W. "Prime Number Race." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PrimeNumberRace.html