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:
By comparison between those limit densities, a number of conjectures may be demonstrated: Twins, Polignac, Consecutive primes, Goldbach…
Above analysis is also leading us to unravel Goldbach Comet hair.