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/* Finds Mersenne primes using the Lucas-Lehmer test
*
* Tom St Denis, tomstdenis@gmail.com
*/
#include <time.h>
#include <tommath.h>
static mp_err is_mersenne(long s, mp_bool *pp)
{
mp_int n, u;
mp_err res;
int k;
*pp = MP_NO;
if ((res = mp_init(&n)) != MP_OKAY) {
return res;
}
if ((res = mp_init(&u)) != MP_OKAY) {
goto LBL_N;
}
/* n = 2^s - 1 */
if ((res = mp_2expt(&n, (int)s)) != MP_OKAY) {
goto LBL_MU;
}
if ((res = mp_sub_d(&n, 1uL, &n)) != MP_OKAY) {
goto LBL_MU;
}
/* set u=4 */
mp_set(&u, 4uL);
/* for k=1 to s-2 do */
for (k = 1; k <= (s - 2); k++) {
/* u = u^2 - 2 mod n */
if ((res = mp_sqr(&u, &u)) != MP_OKAY) {
goto LBL_MU;
}
if ((res = mp_sub_d(&u, 2uL, &u)) != MP_OKAY) {
goto LBL_MU;
}
/* make sure u is positive */
while (u.sign == MP_NEG) {
if ((res = mp_add(&u, &n, &u)) != MP_OKAY) {
goto LBL_MU;
}
}
/* reduce */
if ((res = mp_reduce_2k(&u, &n, 1uL)) != MP_OKAY) {
goto LBL_MU;
}
}
/* if u == 0 then its prime */
if (mp_iszero(&u) == MP_YES) {
mp_prime_is_prime(&n, 8, pp);
if (*pp != MP_YES) printf("FAILURE\n");
}
res = MP_OKAY;
LBL_MU:
mp_clear(&u);
LBL_N:
mp_clear(&n);
return res;
}
/* square root of a long < 65536 */
static long i_sqrt(long x)
{
long x1, x2;
x2 = 16;
do {
x1 = x2;
x2 = x1 - ((x1 * x1) - x) / (2 * x1);
} while (x1 != x2);
if ((x1 * x1) > x) {
--x1;
}
return x1;
}
/* is the long prime by brute force */
static int isprime(long k)
{
long y, z;
y = i_sqrt(k);
for (z = 2; z <= y; z++) {
if ((k % z) == 0)
return 0;
}
return 1;
}
int main(void)
{
mp_bool pp;
long k;
clock_t tt;
k = 3;
for (;;) {
/* start time */
tt = clock();
/* test if 2^k - 1 is prime */
if (is_mersenne(k, &pp) != MP_OKAY) {
printf("Whoa error\n");
return -1;
}
if (pp == MP_YES) {
/* count time */
tt = clock() - tt;
/* display if prime */
printf("2^%-5ld - 1 is prime, test took %ld ticks\n", k, (long)tt);
}
/* goto next odd exponent */
k += 2;
/* but make sure its prime */
while (isprime(k) == 0) {
k += 2;
}
}
}
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