2019/08/16 by William D. Banks, Paul Pollack, Banks, William +3
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1908.06161
openalex publication_date 2019/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A pair of odd primes is said to be symmetric if each prime is congruent to one modulo their difference. A theorem from 1996 by Fletcher, Lindgren, and the third author provides an upper bound on the number of primes up to x that belong to a symmetric pair. In the present paper, that theorem is improved to what is likely to be the best possible result. We also establish that there exist infinitely many symmetric pairs of primes. In fact, we show that for every integer m at least 2 there is a string of m consecutive primes, any two of which form a symmetric pair.