Numbers Theory

Unexplored approach of Prime Numbers

Succinct  presentation

Eliminating from Z all multiples of 2 and 3 provides the set of twins relatively prime to 2 and 3.  We divide that set into two subsets which we christen “juniors” and “elders”. Those are relatively prime and equally infinitely many. Carrying on elimination of successive prime factors, we calculate the corresponding numbers of ‘survivals’.  That approach leads:

• not only to the limit density of whole primes set as was found by Legendre,
• but also to limit densities of a number of primes subsets.

By comparison between those limit densities, a number of conjectures may be demonstrated: Twins, Polignac, Consecutive primes.