Primes of the Form m²+1 and Goldbach's `Other Other' Conjecture

2025/02/05 by Jon Grantham, Grantham, Jon, Hester Graves +1 · 1 citation
Chemistry · Mathematics · #11N32 #11P32 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and advancements in chemistry #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2502.03513

openalex publication_date 2025/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute all primes up to 6.25× 10²⁸ of the form m²+1. Calculations using this list verify, up to our bound, a less famous conjecture of Goldbach. We introduce `Goldbach champions' as part of the verification process and prove conditional results about them, assuming either Schinzel's Hypothesis H or the Bateman-Horn Conjecture.

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