TL;DR
This paper introduces a new sieve method for identifying twin primes of the form 6m±1, leveraging properties of non-rank numbers and primes to analyze twin prime distribution without parity issues.
Contribution
It presents a novel twin prime sieve based on twin ranks and non-ranks, providing a Legendre-type formula for counting twin ranks near primorials.
Findings
Developed a twin prime sieve free of parity problems
Identified and counted non-rank numbers using primes p≥5
Derived a formula for estimating twin ranks near primorials
Abstract
A sieve is constructed for ordinary twin primes of the form 6m+/-1 that are characterized by their twin rank m. It has no parity problem. Non-rank numbers are identified and counted using odd primes p>=5. Twin- and non-ranks make up the set of positive integers. Regularities of non-ranks allow gathering information on them to obtain a Legendre-type formula for the number of twin-ranks near primorial arguments.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAssisted Reproductive Technology and Twin Pregnancy · Genomic variations and chromosomal abnormalities