Chebyshev's bias

Chebyshev's bias refers to the observed tendency that prime numbers—numbers divisible only by 1 and themselves—are more often found in certain types of number patterns than others. Specifically, when comparing the distribution of primes in different arithmetic progressions (like numbers ending in 1 versus 3), there’s a subtle bias: primes tend to appear more frequently in some sequences over large ranges, even though, in theory, they should be evenly distributed. This bias is a nuanced phenomenon arising from deep properties of prime numbers and their distribution, highlighting that prime patterns can show surprising preferences despite overall randomness.