output.txt

primality test using primality_sqrt_bound_coprime_30(int64_t)
L = 100000000 : R = 100100000
test 1 duration : 0.281 s
test 2 duration : 0.225 s
test 3 duration : 0.222 s
test 4 duration : 0.227 s
test 5 duration : 0.226 s
test 6 duration : 0.223 s
test 7 duration : 0.223 s
test 8 duration : 0.225 s
test 9 duration : 0.224 s
test 10 duration : 0.225 s
average of 10 test(s) : 0.2301 s

primality_sqrt_bound_coprime_30.cpp

#include <cmath>

bool primality_sqrt_bound_coprime_30(int64_t a) {
    if(a == 2 || a == 3 || a == 5) return true;
    if(a % 2 == 0 || a % 3 == 0 || a % 5 == 0) return false;
    double lim = sqrt(a);
    /*  0    1    2    3    4    5    6    7    8    9    10    11    12    13    14    15    17    ...
     *        \                           / \                   / \         / \               /\
     *         ---------------------------   -------------------   ---------   ---------------  ----...
     *                      6                        4                 2              4             ...
     *
     * modulo distances between numbers coprime to 30 are stored in s[]
     */
    int s[] = {6, 4, 2, 4, 2, 4, 6, 2};
    for(int i = 7, t = 1; i <= lim; i += s[t], t = ++t & 7)
        if(a % i == 0)
            return false;
    return true;
}