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