output.txt

primality test using primality_sqrt_bound_coprime_6(int64_t)
L = 100000000 : R = 100100000
test 1 duration : 0.278 s
test 2 duration : 0.269 s
test 3 duration : 0.283 s
test 4 duration : 0.258 s
test 5 duration : 0.263 s
test 6 duration : 0.272 s
test 7 duration : 0.262 s
test 8 duration : 0.265 s
test 9 duration : 0.281 s
test 10 duration : 0.274 s
average of 10 test(s) : 0.2705 s

primality_sqrt_bound_coprime_6.cpp

#include <cmath>

bool primality_sqrt_bound_coprime_6(int64_t a) {
    if(a == 2 || a == 3) return true;
    if(a % 2 == 0 || a % 3 == 0) return false;
    double lim = sqrt(a);
    /*  0    1    2    3    4    5    0    1   ...
     *        \                 / \       /
     *         -----------------   -------
     *                 4              2
     * modulo distances between numbers coprime to 6 are stored in s[]
     */
    int s[2] = {4, 2};
    for(int i = 5, t = 1; i <= lim; i += s[t], t = ++t % 2)
        if(a % i == 0)
            return false;
    return true;
}