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Cycles and Patterns in the Sieve of Eratosthenes, Potential Twin Primes

2021/07/14 by George F. Grob, Grob, George F.
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.2107.06950

openalex publication_date 2021/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper analyzes the emergence and distribution of potential twin primes, pairs of integers that are both relatively prime to the first n primes or to a given set M of primes, and which are the breeding grounds of true twin primes. It describes cyclical patterns of their location across the number line and provides a formula for counting them.

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