Bias in the Distribution Of Primes

Abstract

Any model based on the randomness of primes would strongly suggest that every residual class a(mod q) must contain roughly the same number of primes for (a; q) = 1. But despite the obviously seeming flow of logic, the above is inaccurate as a bias is obsereved in the distribution of primes when taken from different residual classes. A bias also exists in the disribution of prime pairs of form (p; p + 2k) where k 2 N. This report is a humble attempt to discover these biases and provide conjuctural explaination of such phenomenons.