Verification of Gilbraith's conjecture up to 10¹⁴

2025/10/08 by Simon Plouffe, Plouffe, Simon
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2510.06688

openalex publication_date 2025/10/08 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

A calculation was performed to verify Proth-Gilbraith's conjecture for all prime numbers up to 0¹⁴. The previous calculation was performed by Andrew Odlyzko in 1993 up to 0¹³. This involves calculating the differences between consecutive primes in absolute value and starting over. The conjecture states that all lines except the first begin with 1. To prove it, it suffices to find a line beginning with 1 and followed only by 0 and 2.

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