2012/04/17 by Hans J. Weber, Weber, H. J.
Mathematics · #11A41 #11N05 #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1204.3795
openalex publication_date 2012/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.