Projecteuler 3 - 最大素数

Question

我很好奇为什么这段代码找不到最大的素因子。 我无法找到数学和/或逻辑错误。

#include <stdio.h>

int compute( int input ) {
    int biggest_primefactor = 1;

    while(input > biggest_primefactor) {
        int i = 2;
        while(input%i != 0) i++; /* find factor, which is a primefactor */
        input /= i;
        if( i > biggest_primefactor) biggest_primefactor = i;
    }
    return biggest_primefactor;
}

void main () {
    unsigned long long int input = 600851475143;
    printf("%d", compute( input ));
}

输出为1