快速计算素数程序

Wheel factorization

Wheel factorization是一种生成素数方法。

对于大于30的数，只有30n+1,30n+7,30n+11,30n+13,30n+17,30n+19,30n+23,30n+29才可能是素数，这里n>=1。

#include <stdio.h>
#include <math.h>

#define NUM_O_PRIMES    2015
long primes1[NUM_O_PRIMES];

void primes()
{
int base = 30, pc = 0, column[] = {1, 7, 11, 13, 17, 19, 23, 29};

int pp = 0;
primes1[pp++] = 2;
primes1[pp++] = 3;
primes1[pp++] = 5;
primes1[pp++] = 7;
primes1[pp++] = 11;
primes1[pp++] = 13;
primes1[pp++] = 17;
primes1[pp++] = 19;
primes1[pp++] = 23;
primes1[pp++] = 29;

while(pp < NUM_O_PRIMES)
{
if(pc == 8)
{
base += 30;
pc = 0;
}

long p, q;
p = base + column[pc++];
q = sqrt(p);
int j = 3;
while(primes1[j] <= q)
{
if(p % primes1[j] == 0)
break;
j++;
}
if(primes1[j] > q)
primes1[pp++] = p;
}
}

int main(void)
{
primes();
int i;
for(i=0; i<NUM_O_PRIMES; i++)
{
printf("%d:%ld\n", i+1, primes1[i]);
}
return 0;
}