The set of primes: Towards an optimized algorithm, prime generationand validation, and asymptotic consequences

摘要

Starting from the result that the prime distribution is deterministic, we show in its maxi-mal reduced form, the set of prime numbers P. This set can be expressed in terms of twosubsets of NI using three specific selection rules, acting on two sets of prime candidates.The asymptotic behaviour is considered too. We go head towards an optimized algorithmto generate primes, whose computational complexity is C(n) ∈0(n). In addition a pre-com-puted algorithm is also considered and its computational complexity C(n) ∈ 0(1).