Sieves for Twin Primes in Class I

Details Sieves for Twin Primes in Class I Sieves for Twin Primes in Class I

2012-04-25

arxiv.org/abs/1204.5728v1

Mathematics

Number Theory

16 pages. To be submitted. arXiv admin note: substantial text overlap with arXiv:1204.3795 and arXiv:1203.5240

Scientific paper

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.

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