Sieves for Twin Primes in Class I
arXiv:1204.5728
Abstract
Sieves are constructed for twin primes in class I, which are of the form 2m+/-D, D>=3 odd. They are characterized by their twin-D-I rank m. They have no parity problem. Non-rank numbers are identified and counted using odd primes p>=5. Twin-D-I ranks and non-ranks make up the set of positive integers. Regularities of non-ranks allow obtaining the number of twin-D-I ranks. It involves considerable cancellations so that the asymptotic form of its main term collapses to the expected form, but its coefficient depends on D.
16 pages. Overall D-dependent factor corrected. arXiv admin note: substantial text overlap with arXiv:1204.3795 and arXiv:1203.5240