一个推广的Lucas型素性测定算法

A Generalized Lucasian Primality Test

特殊形式的自然数,例如形式为Mh,n=h.2n±1的数(h奇数,n正整数)常是人们感兴趣的研究对象。Berrizbeitia和Berry提出一个Lucass型素性测定测试,即当h mod 5时测试Mh,n的素性所用的种子仅依赖于h。本文推广了Berrizbeitia和Berry关于Mh,n=h.2n±1的素性测定,即将h不能被5整除推广到h不能被形如4m+1的素数q整除时的情形(特别当h能被15整除时)。

Numbers of special form, such as Mh,n = h · 2^n ＋ 1 （h, n positive integers with h odd）, are often interested by mathematicians. Berrizbeitia and Berry present a test which allows one to test primality of Mh,n =h · 2^n ± 1 by means of a Lucasian sequence with a seed determined only by h , h absolotely uneqvalto mod 5. We present a primality test of the form Mh,n =h · 2^n= 1 （in particular with h divisible by 15） ,which generalizes Berrizbeitia and Berry＇s test for such numbers with h ≠ 0 mod 5.