质数判定的二次剩余法

The Method of Quadratic Residue for Prime Judgement

在n^2±p型整数的质约数的基础上,进一步将结论推广到一般情况:对于任意一个正整数a,得出n^2±a型整数的质约数的全部类数,同时也给出求解n^2±a型整数的所有可能的质约数的一般解法。这种方法,可应用于判定一个整数是否是质数,而成为一种新的、改进的Erastosthenes筛法。

Baseed on the prime divisors of n^2±p type integer number, this paper further expande the conclusion into general conditions: for any positive integer number 'a', all kinds of the prime divisors of the n^2±a type integer number are found and, in the mean- while, a general solution to finding all possible prime divisors of n^2±a type integer number is presented. This method can be applied to judge whether an integer number is a prime number and thus it becomes a new improved Erastosthenes sieve method.