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Overhaul of the prime-tests
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 - Removal of the Fermat test mp_prime_fermat
 - Replacement of the Strong Lucas-Selfridge test with the
   Extra Strong Lucas test with Robert Baillie's parameters
   P = 3 and Q = 1
 - Finer grained early-outs
 - All determistic tests < 2^64 empirically verified
 - Additional tests to check the implementations of the
   Miller-Rabin and Extra Strong Lucas tests
 - Addition of tests of the LTM_USE_ONLY_MR to the CI
 - Documentation update
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@czurnieden
czurnieden committed Jul 1, 2024
1 parent 5809141 commit 681dc56
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8 changes: 4 additions & 4 deletions .github/workflows/main.yml
View file
Original file line number Diff line number Diff line change
Expand Up @@ -58,13 +58,13 @@ jobs:
# Run always with valgrind (no sanitizer, but debug info)
- { BUILDOPTIONS: '--with-cc=gcc --with-m64 --with-valgrind', SANITIZER: '', COMPILE_DEBUG: '1', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: '' }
# Alternative big-int version of mp_log(_n)
- { BUILDOPTIONS: '--with-cc=gcc --with-m64 --cflags=-DS_MP_WORD_TOO_SMALL_C="" --with-valgrind', SANITIZER: '', COMPILE_DEBUG: '1', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: '' }
- { BUILDOPTIONS: '--with-cc=gcc --with-m64 --cflags=-DS_MP_WORD_TOO_SMALL_C="" --cflags=-DLTM_USE_ONLY_MR --with-valgrind', SANITIZER: '', COMPILE_DEBUG: '1', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: '' }
# Shared library build
- { BUILDOPTIONS: '--with-cc=gcc --make-option=-f --make-option=makefile.shared', SANITIZER: '', COMPILE_DEBUG: '0', COMPILE_LTO: '1', CONV_WARNINGS: '', OTHERDEPS: 'libtool-bin' }
# GCC for the 32-bit architecture (no valgrind)
- { BUILDOPTIONS: '--with-cc=gcc --with-m32', SANITIZER: '', COMPILE_DEBUG: '0', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: 'libc6-dev-i386 gcc-multilib' }
# Alternative big-int version of mp_log(_n) for the 32-bit architecture (no valgrind)
- { BUILDOPTIONS: '--with-cc=gcc --with-m32 --cflags=-DS_MP_WORD_TOO_SMALL_C="" ', SANITIZER: '', COMPILE_DEBUG: '0', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: 'libc6-dev-i386 gcc-multilib' }
- { BUILDOPTIONS: '--with-cc=gcc --with-m32 --cflags=-DS_MP_WORD_TOO_SMALL_C="" --cflags=-DLTM_USE_ONLY_MR ', SANITIZER: '', COMPILE_DEBUG: '0', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: 'libc6-dev-i386 gcc-multilib' }
# clang for the 32-bit architecture (no valgrind)
- { BUILDOPTIONS: '--with-cc=clang-10 --with-m32', SANITIZER: '', COMPILE_DEBUG: '0', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: 'clang-10 llvm-10 gcc-multilib' }
# RSA superclass with tests (no sanitizer, but debug info)
Expand Down Expand Up @@ -128,8 +128,8 @@ jobs:
- { BUILDOPTIONS: '--with-cc=gcc --cflags=-DMP_16BIT --limit-valgrind', SANITIZER: '1', COMPILE_DEBUG: '0', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: '' }
- { BUILDOPTIONS: '--with-cc=gcc --cflags=-DMP_32BIT --limit-valgrind', SANITIZER: '1', COMPILE_DEBUG: '0', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: '' }
# Alternative big-int version of mp_log(_n)
- { BUILDOPTIONS: '--with-cc=gcc --cflags=-DMP_16BIT --cflags=-DS_MP_WORD_TOO_SMALL_C="" --limit-valgrind', SANITIZER: '1', COMPILE_DEBUG: '0', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: '' }
- { BUILDOPTIONS: '--with-cc=gcc --cflags=-DMP_32BIT --cflags=-DS_MP_WORD_TOO_SMALL_C="" --limit-valgrind', SANITIZER: '1', COMPILE_DEBUG: '0', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: '' }
- { BUILDOPTIONS: '--with-cc=gcc --cflags=-DMP_16BIT --cflags=-DS_MP_WORD_TOO_SMALL_C="" --cflags=-DLTM_USE_ONLY_MR --limit-valgrind', SANITIZER: '1', COMPILE_DEBUG: '0', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: '' }
- { BUILDOPTIONS: '--with-cc=gcc --cflags=-DMP_32BIT --cflags=-DS_MP_WORD_TOO_SMALL_C="" --cflags=-DLTM_USE_ONLY_MR --limit-valgrind', SANITIZER: '1', COMPILE_DEBUG: '0', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: '' }

# clang for the x86-64 architecture with restricted limb sizes
- { BUILDOPTIONS: '--with-cc=clang --cflags=-DMP_16BIT --limit-valgrind', SANITIZER: '1', COMPILE_DEBUG: '0', COMPILE_LTO: '0', CONV_WARNINGS: '', OTHERDEPS: 'clang llvm' }
Expand Down
304 changes: 300 additions & 4 deletions demo/test.c
View file
Original file line number Diff line number Diff line change
Expand Up @@ -894,7 +894,7 @@ static int test_mp_prime_rand(void)

/* test for size */
for (ix = 10; ix < 128; ix++) {
printf("Testing (not safe-prime): %9d bits \n", ix);
printf("\rTesting (not safe-prime): %9d bits ", ix);
fflush(stdout);
DO(mp_prime_rand(&a, 8, ix, (rand_int() & 1) ? 0 : MP_PRIME_2MSB_ON));
EXPECT(mp_count_bits(&a) == ix);
Expand All @@ -907,15 +907,264 @@ static int test_mp_prime_rand(void)
return EXIT_FAILURE;
}

/* Some small pseudoprimes to test the individual implementations */

/* Miller-Rabin base 2 */
static const uint32_t SPSP_2[] = {
2047, 3277, 4033, 4681, 8321, 15841, 29341, 42799,
49141, 52633, 65281, 74665, 80581, 85489, 88357, 90751
};

/* Miller-Rabin base 3 */
static const uint32_t SPSP_3[] = {
121, 703, 1891, 3281, 8401, 8911, 10585, 12403, 16531,
18721, 19345, 23521, 31621, 44287, 47197, 55969, 63139,
74593, 79003, 82513, 87913, 88573, 97567
};

/* SPSP to all bases < 100 */
static const char *SPSP_2_100_LARGE[4] = {
"3L2x7YRmz7g4q+DwxESBacAClxrNiuspLCf8BUEphtky+5VNHLAb2ZZLLI0bu6cAOtNkUXenakBCCL"
"Vn7gqOpkcrQ/ptxZdk+4gnI99wFjgcfM512N71ZzbwvLe+5Pzat2k+nHIjE0w/WbQvzk4a2/syAY8S"
"i1B5XRjXYVAQOLyNWhsFpXeWXUgqiNzv7avfwBA3ZOXt", /* bases 2 - 100 */
"JOcSIwxGqGEjeQ2GsdlnFMwhc+xY7EtZo5Kf4BglOuakxTJaP8qrdZyduXaAZUdzyPgQLf7B8vqvVE"
"VLJwH7dLkLEiw19tfu3naT6DgQWzk+b5WuwWJzsTMdgWWH86M1h/Gjt2J/qABtTTH26C8bS4v/q9Fh"
"R8jqHNOiufUgHkDQdW9Z+BLlf6OVVh2VwPIOGVc7kFF", /* bases 2 - 107 */
"1ZCddPKHO7yeqI5ZeKG5ssTnzJeIDpWElJEZnHwejl4tsyly44JgwdiRmXgsi9FQfYhMzFZMgV6qWZZ"
"sIJl4RNgpD/PDb3nam++ECkzMBuNIXVpmZzw+Gj5xQmpKK+OX8pFSy2IQiKyKAOfSaivXEb2/dga2J/"
"Pc2d23lw+eP3WtBbfHc7TAQGgNI/6Xmcpl1G64eXCrJ", /* bases 2 - 103 */
"cCax282DurA+2Z54W3VLKSC2mwgpilQpGydCDHvXHNRKbJQRa5NtLLfa3sXvCmUWZ9okP2ZSsPDnw0X"
"dUQLzaz59vnw0rKbfsoA4nDBjMXR78Q889+KS4HFKfXkzxsiIKYo0kSfwPKYxFUi4Zj185kwwAPTAr2"
"IjegdWjQLeX1ZQM0HVUUF3WEVhHXcFzF0sMiJU5hl" /* bases 2 - 101 */
};

#ifndef LTM_USE_ONLY_MR
/* Extra strong Lucas test with Baillie's parameters Q = 1, P = 3 */
static const uint32_t ESLPSP[] = {
989, 3239, 5777, 10877, 27971, 29681, 30739, 31631, 39059, 72389,
73919, 75077, 100127, 113573, 125249, 137549, 137801, 153931, 155819,
161027, 162133, 189419, 218321, 231703, 249331, 370229, 429479, 430127,
459191, 473891, 480689, 600059, 621781, 632249, 635627
};

/*
Almost extra strong Lucas test with Baillie's parameters Q = 1, P = 3
Only those that are not in ESLPSP.
*/
static const uint32_t AESLPSP[] = {
10469, 154697, 233659, 472453, 629693, 852389, 1091093, 1560437,
1620673, 1813601, 1969109, 2415739, 2595329, 2756837, 3721549,
4269341, 5192309, 7045433, 7226669, 7265561
};
#endif

/* Some randomly choosen 200 decimal digit large primes (https://primes.utm.edu/lists/small/small2.html) */
static const char *medium_primes[10] = {
"C8Ckh0vviS3HUPdB1NSrSm+gOodw/f1aQ5+aaH1W6RMB0jVkO6lTaL54O3o7U5BSGUFGxm5gAvisbJamasuLZS8g3ZsJ2JM4Vtn9cQZRfkP6b8V",
"64xDN9FqLBiovZ/9q/EPm0DONpIfn5MbJKHa+IjT0fjAzkg34FpAmad+CwhcpKaiTbZEpErut+DhpVyiQfqBFrgcGnGhhIrMF/XkyY3aVx6E96B",
"8cyuMlENm0vh/eWwgHUpDKqmLyCSsRQZRWvbHpA2jHDZv1EhHkVhceg3OFRZn/aXRBnbdtsc2xO6sWh9KZ5Mo7u9rJgBJMVtDnu094MCExj1YvB",
"BRFZFsYjSz45un8qptnuSqEsy9wV0BzbMpVAB1TrwImENOVIc1cASZNQ/mXG2xtazqgn/juVzFo91XLx9PtIlkcK0L2T6fBNgy8Lc7dSVoKQ+XP",
"Ez/mDl+to2gm69+VdIHI9Q7vaO3DuIdLVT69myM3HYwVBE+G24KffAOUAp3FGrSOU+LtERMiIYIEtxPI7n/DRJtmL2i0+REwGpTMge2d2EpabfB",
"5+Uz1gPFjZJ/nNdEOmOaMouJSGzygo42qz7xOwXn/moSUvBpPjo4twRGbK0+qaeU/RI8yYYxXr3OBP4w+/jgL3mN9GiENDM5LtEKMiQrZ9jIVEb",
"AQ5nD1+G1grv41s/XlK+0YTGyZgr/88PzdQJ8QT9tavisTgyG6k8/80A4HQhnFndskHNAaB2EW5fE7KH3kk7m89s8JnVqkJyGZWSfs1+JlmHLPf",
"3F19vPmM0Ih89KZ04Xmd62QB9F6E2sztT10A7Kcqc44eKvsNHh+JY6Z6gJXkbWg1Iw7xr29QAhEF/o1YAgfutQtpdzHkex06Yd71kPsaZdKXiC5",
"2fIcJ1t/VYCColXGs+ji/txNMEXn2FXdowLzlo7QKqzAWHdAbwtltSO5qpSp3OUiEOGUUi3hbyw3iQRE8nFJaikJ89Wdox6vpPtIsc3QRjexMnv",
"8aOicQ5gIbFCarFUgSgzh40LpuZ0jjK1u48/YT+C0h1dAQ8CIEgZjHZT+5/7cCRGmJlo+XCp7S41MSQ2ZNRSJh2texRYtvAXBAZfR8A8twl316P"
};

const mp_digit prime_tab[] = {
0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083,
0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,

0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,

0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,

0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
};

#define ARR_LENGTH(a) ((int)(sizeof((a))/sizeof((a)[0])))

static int test_mp_prime_miller_rabin(void)
{
mp_int a, b, c;
bool result;
int i;
mp_digit j;
DOR(mp_init_multi(&a, &b, &c, NULL));

/* SPSP to base 2 */
mp_set(&b, 2u);
for (i = 0; i < ARR_LENGTH(SPSP_2); i++) {
result = false;
mp_set_u32(&a, SPSP_2[i]);
DO(mp_prime_miller_rabin(&a, &b, &result));
EXPECT(result == true);
}

/* Some larger primes to check for false negatives */
for (i = 0; i < 10; i++) {
result = false;
DO(mp_read_radix(&a, medium_primes[i], 64));
DO(mp_prime_miller_rabin(&a, &b, &result));
EXPECT(result == true);
}
/* Some semi-primes */
for (i = 0; i < 5; i += 2) {
result = false;
DO(mp_read_radix(&a, medium_primes[i], 64));
DO(mp_read_radix(&c, medium_primes[i+1], 64));
DO(mp_mul(&a, &c, &a));
DO(mp_prime_miller_rabin(&a, &b, &result));
EXPECT(result == false);
}

/* SPSP to base 3 */
mp_set(&b, 3u);
for (i = 0; i < ARR_LENGTH(SPSP_3); i++) {
result = false;
mp_set_u32(&a, SPSP_3[i]);
DO(mp_prime_miller_rabin(&a, &b, &result));
EXPECT(result == true);
}

/* SPSP to bases 2 -- 100 */
mp_set(&b, 2u);
for (i = 0; i < 4; i++) {
DO(mp_read_radix(&a, SPSP_2_100_LARGE[i], 64));
for (j = 2u; j <= 100u; j++) {
result = false;
mp_set(&b, j);
DO(mp_prime_miller_rabin(&a, &b, &result));
EXPECT(result == true);
}
/* 107 is a prime that works */
mp_set(&b, 107u);
DO(mp_prime_miller_rabin(&a, &b, &result));
EXPECT(result == false);
}

/* SPSP to bases 2 -- 100, automatic */
mp_set(&b, 2u);
for (i = 0; i < 4; i++) {
DO(mp_read_radix(&a, SPSP_2_100_LARGE[i], 64));
for (j = 2u; j <= (mp_digit)mp_prime_rabin_miller_trials(mp_count_bits(&a)); j++) {
result = false;
mp_set(&b, (mp_digit)prime_tab[j]);
DO(mp_prime_miller_rabin(&a, &b, &result));
}
/* These numbers are not big enough for the heuristics to work */
EXPECT(result == true);
}

mp_clear_multi(&a, &b, &c, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, &c, NULL);
return EXIT_FAILURE;
}

#ifndef LTM_USE_ONLY_MR
static int test_mp_prime_extra_strong_lucas(void)
{
mp_int a, b;
bool result;
int i;

DOR(mp_init_multi(&a, &b, NULL));

/* Check Extra Strong pseudoprimes */
for (i = 0; i < ARR_LENGTH(ESLPSP); i++) {
result = false;
mp_set_u32(&a, ESLPSP[i]);
DO(mp_prime_extra_strong_lucas(&a, &result));
EXPECT(result == true);
}

/* Check Almost Extra Strong pseudoprimes (not in ESLPSP) */
for (i = 0; i < ARR_LENGTH(AESLPSP); i++) {
result = false;
mp_set_u32(&a, AESLPSP[i]);
DO(mp_prime_extra_strong_lucas(&a, &result));
EXPECT(result == false);
}

/* Some larger primes to check for false negatives */
for (i = 0; i < 10; i++) {
result = false;
DO(mp_read_radix(&a, medium_primes[i], 64));
DO(mp_prime_extra_strong_lucas(&a, &result));
EXPECT(result == true);
}

/* Some semi-primes */
for (i = 0; i < 5; i++) {
result = false;
DO(mp_read_radix(&a, medium_primes[i], 64));
DO(mp_read_radix(&a, medium_primes[i+1], 64));
DO(mp_mul(&a, &b, &a));
DO(mp_prime_extra_strong_lucas(&a, &result));
EXPECT(result == false);
}

mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
LBL_ERR:
mp_clear_multi(&a, &b, NULL);
return EXIT_FAILURE;
}
#endif

static int test_mp_prime_is_prime(void)
{
int ix;
mp_err e;
bool cnt, fu;
bool cnt;
#ifndef LTM_USE_ONLY_MR
bool fu;
#endif

mp_int a, b;
DOR(mp_init_multi(&a, &b, NULL));

/* strong Miller-Rabin pseudoprimes to the first 100 primes (gernerated with Arnault's method) */
printf("Testing mp_prime_is_prime() with SPSPs to the first 100 primes\n");
for (ix = 0; ix < 4; ix++) {
DO(mp_read_radix(&a,SPSP_2_100_LARGE[ix],64));
DO(mp_prime_is_prime(&a, mp_prime_rabin_miller_trials(mp_count_bits(&a)), &cnt));
if (cnt) {
printf("SPSP_2_100_LARGE[%d] is not prime but mp_prime_is_prime says it is.\n", ix);
goto LBL_ERR;
}
}

/* strong Miller-Rabin pseudoprime to the first 200 primes (F. Arnault) */
printf("Testing mp_prime_is_prime() with Arnault's pseudoprime 803...901");
DO(mp_read_radix(&a,
Expand Down Expand Up @@ -959,6 +1208,7 @@ static int test_mp_prime_is_prime(void)
DO(mp_prime_is_prime(&b, mp_prime_rabin_miller_trials(mp_count_bits(&b)), &cnt));
/* large problem */
EXPECT(cnt);
#ifndef LTM_USE_ONLY_MR
DO(mp_prime_frobenius_underwood(&b, &fu));
EXPECT(fu);
if ((e != MP_OKAY) || !cnt) {
Expand All @@ -970,13 +1220,14 @@ static int test_mp_prime_is_prime(void)
putchar('\n');
goto LBL_ERR;
}

#endif
}
#ifndef LTM_USE_ONLY_MR
/* Check regarding problem #143 */
DO(mp_read_radix(&a,
"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9A63A3620FFFFFFFFFFFFFFFF",
16));
DO(mp_prime_strong_lucas_selfridge(&a, &cnt));
DO(mp_prime_extra_strong_lucas(&a, &cnt));
/* large problem */
EXPECT(cnt);
if ((e != MP_OKAY) || !cnt) {
Expand All @@ -985,6 +1236,47 @@ static int test_mp_prime_is_prime(void)
putchar('\n');
goto LBL_ERR;
}
#endif
/* Check deterministic tests */
#ifdef LTM_USE_ONLY_MR
#if ((defined S_MP_PRIME_IS_DIVISIBLE_C) && (MP_PRIME_TAB_SIZE >= 256))
/* 2-SPRP 4188889 = 431 * 9719 < 2^22 */
DO(mp_read_radix(&a,"4188889",10));
DO(mp_prime_is_prime(&a, 0, &cnt));
EXPECT(cnt == false);
/* Last prime < 2^22 */
DO(mp_read_radix(&a,"4194301",10));
DO(mp_prime_is_prime(&a, 0, &cnt));
EXPECT(cnt == true);
/* 2,3-SPRP 6787327 = 1303 * 5209 < 2^23 */
DO(mp_read_radix(&a,"6787327",10));
DO(mp_prime_is_prime(&a, 0, &cnt));
EXPECT(cnt == false);
/* Last prime < 2^23 */
DO(mp_read_radix(&a,"8388593",10));
DO(mp_prime_is_prime(&a, 0, &cnt));
EXPECT(cnt == true);

/* 2,3,1459-SPRP < 2^32*/
DO(mp_read_radix(&a,"1518290707",10));
DO(mp_prime_is_prime(&a, -1, &cnt));
EXPECT(cnt == false);
#endif
/* 2,3,7,61-SPRP < 2^43*/
DO(mp_read_radix(&a,"7038007247701",10));
DO(mp_prime_is_prime(&a, -1, &cnt));
EXPECT(cnt == false);

/* 2,325,9375,28178,450775,9780504-SPRP < 2^64
which is also a
2,3,325,9375,28178,450775,9780504-SPRP
*/
DO(mp_read_radix(&a,"18411296009130176041",10));
DO(mp_prime_is_prime(&a, -1, &cnt));
EXPECT(cnt == false);

#endif


mp_clear_multi(&a, &b, NULL);
return EXIT_SUCCESS;
Expand Down Expand Up @@ -2579,6 +2871,10 @@ static int unit_tests(int argc, char **argv)
T1(mp_montgomery_reduce, MP_MONTGOMERY_REDUCE),
T1(mp_root_n, MP_ROOT_N),
T1(mp_or, MP_OR),
#ifndef LTM_USE_ONLY_MR
T1(mp_prime_extra_strong_lucas, MP_PRIME_EXTRA_STRONG_LUCAS),
#endif
T1(mp_prime_miller_rabin, MP_PRIME_MILLER_RABIN),
T1(mp_prime_is_prime, MP_PRIME_IS_PRIME),
T1(mp_prime_next_prime, MP_PRIME_NEXT_PRIME),
T1(mp_prime_rand, MP_PRIME_RAND),
Expand Down
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