Verification of Gilbraith's conjecture up to 10$^{14}$

Abstract

A calculation was performed to verify Proth-Gilbraith's conjecture for all prime numbers up to 0$^{14}$. The previous calculation was performed by Andrew Odlyzko in 1993 up to 0$^{13}$. 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.