The first case of Fermat’s last theorem is true for all prime exponents up to 714,591,416,091,389

Abstract

We show that if the first case of Fermat’s Last Theorem is false for prime exponent p p then p 2 {p^2} divides q p − q {q^p} - q for all primes q ⩽ 8 q q \leqslant 8q . As a corollary we state the theorem of the title.