English

Sieves for Twin Primes in Class I

Number Theory 2012-05-18 v3

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.

Keywords

Cite

@article{arxiv.1204.5728,
  title  = {Sieves for Twin Primes in Class I},
  author = {H. J. Weber},
  journal= {arXiv preprint arXiv:1204.5728},
  year   = {2012}
}

Comments

16 pages. Overall D-dependent factor corrected. arXiv admin note: substantial text overlap with arXiv:1204.3795 and arXiv:1203.5240

R2 v1 2026-06-21T20:54:44.516Z