145 lines
2.3 KiB
C
145 lines
2.3 KiB
C
/* Finds Mersenne primes using the Lucas-Lehmer test
|
|
*
|
|
* Tom St Denis, tomstdenis@gmail.com
|
|
*/
|
|
#include <time.h>
|
|
#include <tommath.h>
|
|
|
|
int
|
|
is_mersenne (long s, int *pp)
|
|
{
|
|
mp_int n, u;
|
|
int res, k;
|
|
|
|
*pp = 0;
|
|
|
|
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, s)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
|
|
/* set u=4 */
|
|
mp_set (&u, 4);
|
|
|
|
/* 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, 2, &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, 1)) != MP_OKAY) {
|
|
goto LBL_MU;
|
|
}
|
|
}
|
|
|
|
/* if u == 0 then its prime */
|
|
if (mp_iszero (&u) == 1) {
|
|
mp_prime_is_prime(&n, 8, pp);
|
|
if (*pp != 1) printf("FAILURE\n");
|
|
}
|
|
|
|
res = MP_OKAY;
|
|
LBL_MU:mp_clear (&u);
|
|
LBL_N:mp_clear (&n);
|
|
return res;
|
|
}
|
|
|
|
/* square root of a long < 65536 */
|
|
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 */
|
|
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)
|
|
{
|
|
int 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 == 1) {
|
|
/* count time */
|
|
tt = clock () - tt;
|
|
|
|
/* display if prime */
|
|
printf ("2^%-5ld - 1 is prime, test took %ld ticks\n", k, tt);
|
|
}
|
|
|
|
/* goto next odd exponent */
|
|
k += 2;
|
|
|
|
/* but make sure its prime */
|
|
while (isprime (k) == 0) {
|
|
k += 2;
|
|
}
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/* ref: $Format:%D$ */
|
|
/* git commit: $Format:%H$ */
|
|
/* commit time: $Format:%ai$ */
|