1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
|
/* 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;
}
/* $Source$ */
/* $Revision$ */
/* $Date$ */
|
