坎特伯雷难题集中全一数R19是素数的证明

Proof That Repunit R19 in the Canterbury Problem Set Is a Prime Number

摘要: 一个正整数的素性判别是数论中一个有意义和有兴趣的问题，全一数R19是否是一个素数的问题虽在文献中提到已被用n−1法解决，但国内一直未见有证明方法的介绍，本文借助于数学软件Mathematica12.0用个人计算机证明了坎特伯雷难题集中全一数R19是一个素数。这对证明其他整数的素性判定提供了一个参考。

Abstract: The primality criterion of a positive integer is a meaningful and interesting problem in number theory. Although the question of whether Repunit R19 is a prime has been solved by then−1method in literature, there is no introduction to a proven method in China. This article uses the mathematical software Mathematical12.0 to prove on a personal computer that the Repunit R19 in the Canterbury problem set is a prime number. This provides a reference for proving the primality of other integers.