A Sieve for Cousin Primes
arXiv:1204.3795
Abstract
A sieve is constructed for twin primes at distance 4, which are of the form 3(2m+1)+/-2, and are characterized by their twin-4 rank 2m+1. It has no parity problem. Non-ranks are identified as all other odd numbers and counted using odd primes p>=5. Twin-4 ranks and non-ranks make up the set of odd numbers. Regularities of non-ranks allow gathering information on them to obtain a Legendre-type sum for the number of twin-4 ranks. Due to considerable cancellations in it, the asymptotic law of its main term has the expected form and magnitude of its coefficient.
18 pages. A clarification added to, a misstatement removed from introduction. arXiv admin note: substantial text overlap with arXiv:1203.5240