粗略验证“素数定理”
前几日读了卢昌海的《黎曼猜想漫谈》，写的挺好，虽然我这个数学系的也看不大懂。其中有个关于高斯的故事让我崇拜不已：高斯在15岁的时候就发现了粗略的“素数定理”，真不愧是“数学王子”。刚好现在学习C语言，就粗略的验证一下高斯发现的粗略的“素数定理”：
/*
* 粗略检验素数分布密度与指数函数倒数的关系
*/
#include <stdio.h>
#include <math.h>
#define LENGTH 1000
int prime_judge(long num)
{
long temp = sqrt(num) + 1;
long i, test = 0;
for (i = 2; i <= temp ; i++) {
if (num%i == 0)
test++;
}
return test;
}
int print_test(void)
{
long interval_begin, i;
long prime_num = 0;
double destiny, exponent;
printf("Please input an integer: ");
scanf("%ld", &interval_begin);
if (interval_begin == 0)
return 1;
for (i = interval_begin; i <= interval_begin+LENGTH; i++) {
prime_num += !prime_judge(i);
}
destiny = (double) prime_num/LENGTH;
exponent = 1/log(interval_begin+LENGTH/2.0);
printf("%f %f\n", destiny, exponent);
return 0;
}
int main(void)
{
while (print_test() == 0)
;
return 0;
}
只验证了较小的数，但结论还是很清晰的：
素数分布密度和指数函数倒数之差虽然不是越来越小的，但是总体上差数保持在一个较小的范围，再次膜拜一下高斯。
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