def test_with_big_composites(self):
# NextPrime[2^256]-2 (factors: 71, 1559, 4801, 7703, 28286...8993)
self.assertFalse(
isPrime(
115792089237316195423570985008687907853269984665640564039457584007913129640233
- 2))
# NextPrime[2^256]+2 (factors: 3^2, 5, 7, 11, 1753, 19063..7643)
self.assertFalse(
isPrime(
115792089237316195423570985008687907853269984665640564039457584007913129640233
+ 2))
# NextPrime[2^1024]-2
self.assertFalse(
isPrime(
179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137859
- 2))
# NextPrime[2^1024]+2
self.assertFalse(
isPrime(
179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137859
+ 2))
# NextPrime[NextPrime[2^512]]*NextPrime[2^512]
self.assertFalse(
isPrime(
179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639477074095512480796227391561801824887394139579933613278628104952355769470429079061808809522886423955917442317693387325171135071792698344550223571732405562649211
))
def test_with_big_composites(self):
# NextPrime[2^256]-2 (factors: 71, 1559, 4801, 7703, 28286...8993)
self.assertFalse(isPrime(115792089237316195423570985008687907853269984665640564039457584007913129640233-2))
# NextPrime[2^256]+2 (factors: 3^2, 5, 7, 11, 1753, 19063..7643)
self.assertFalse(isPrime(115792089237316195423570985008687907853269984665640564039457584007913129640233+2))
# NextPrime[2^1024]-2
self.assertFalse(isPrime(179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137859-2))
# NextPrime[2^1024]+2
self.assertFalse(isPrime(179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137859+2))
# NextPrime[NextPrime[2^512]]*NextPrime[2^512]
self.assertFalse(isPrime(179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639477074095512480796227391561801824887394139579933613278628104952355769470429079061808809522886423955917442317693387325171135071792698344550223571732405562649211))
def test_with_big_primes(self):
# NextPrime[2^256]
self.assertTrue(
isPrime(
115792089237316195423570985008687907853269984665640564039457584007913129640233
))
# NextPrime[2^1024]
self.assertTrue(
isPrime(
179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137859
))
def test_with_big_primes(self):
# NextPrime[2^256]
self.assertTrue(isPrime(115792089237316195423570985008687907853269984665640564039457584007913129640233))
# NextPrime[2^1024]
self.assertTrue(isPrime(179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137859))
def test_with_hard_primes_to_test(self):
# XXX Rabin-Miller fails to properly detect following composites
with self.assertRaises(AssertionError):
for i in range(100):
# OEIS A014233
self.assertFalse(isPrime(2047))
self.assertFalse(isPrime(1373653))
self.assertFalse(isPrime(25326001))
self.assertFalse(isPrime(3215031751))
self.assertFalse(isPrime(2152302898747))
self.assertFalse(isPrime(3474749660383))
self.assertFalse(isPrime(341550071728321))
self.assertFalse(isPrime(341550071728321))
self.assertFalse(isPrime(3825123056546413051))
self.assertFalse(isPrime(3825123056546413051))
self.assertFalse(isPrime(3825123056546413051))
def test_with_small_composites(self):
self.assertFalse(isPrime(4))
self.assertFalse(isPrime(6))
self.assertFalse(isPrime(9))
self.assertFalse(isPrime(10))
def test_with_small_primes(self):
self.assertTrue(isPrime(3))
self.assertTrue(isPrime(5))
self.assertTrue(isPrime(7))
self.assertTrue(isPrime(11))
def test_getRandomSafePrime(self):
r = getRandomSafePrime(20)
self.assertEqual(numBits(r), 20)
self.assertTrue(isPrime(r))
self.assertTrue(isPrime((r-1)//2))
def test_getRangomPrime(self):
r = getRandomPrime(20)
self.assertEqual(numBits(r), 20)
self.assertTrue(isPrime(r))
def test_with_hard_primes_to_test(self):
# XXX Rabin-Miller fails to properly detect following composites
with self.assertRaises(AssertionError):
for i in range(100):
# OEIS A014233
self.assertFalse(isPrime(2047)) # base 1
self.assertFalse(isPrime(1373653)) # base 2
self.assertFalse(isPrime(25326001)) # base 3
self.assertFalse(isPrime(3215031751)) # base 4
self.assertFalse(isPrime(2152302898747)) # base 5
self.assertFalse(isPrime(3474749660383)) # base 6
self.assertFalse(isPrime(341550071728321)) # base 7
self.assertFalse(isPrime(341550071728321)) # base 8
self.assertFalse(isPrime(3825123056546413051)) # base 9
self.assertFalse(isPrime(3825123056546413051)) # base 10
self.assertFalse(isPrime(3825123056546413051)) # base 11
# Zhang (2007)
self.assertFalse(isPrime(318665857834031151167461)) # base 12
self.assertFalse(isPrime(3317044064679887385961981)) # base 13
# base 14
self.assertFalse(isPrime(6003094289670105800312596501))
# base 15
self.assertFalse(isPrime(59276361075595573263446330101))
# base 16
self.assertFalse(isPrime(564132928021909221014087501701))
# base 17
self.assertFalse(isPrime(564132928021909221014087501701))
# base 18
self.assertFalse(isPrime(1543267864443420616877677640751301))
# base 19
self.assertFalse(isPrime(1543267864443420616877677640751301))
# F. Arnault "Constructing Carmichael Numbers Which Are Strong
# Pseudoprimes to Several Bases". Journal of Symbolic
# Computation. 20 (2): 151-161. doi:10.1006/jsco.1995.1042.
# Section 4.4 Large Example (a pseudoprime to all bases up to
# 300)
p = int("29 674 495 668 685 510 550 154 174 642 905 332 730 "
"771 991 799 853 043 350 995 075 531 276 838 753 171 "
"770 199 594 238 596 428 121 188 033 664 754 218 345 "
"562 493 168 782 883".replace(" ", ""))
self.assertTrue(isPrime(p))
self.assertFalse(p * (313 * (p - 1) + 1) * (353 * (p - 1) + 1))
def test_with_hard_primes_to_test(self):
# XXX Rabin-Miller fails to properly detect following composites
with self.assertRaises(AssertionError):
for i in range(100):
# OEIS A014233
self.assertFalse(isPrime(2047)) # base 1
self.assertFalse(isPrime(1373653)) # base 2
self.assertFalse(isPrime(25326001)) # base 3
self.assertFalse(isPrime(3215031751)) # base 4
self.assertFalse(isPrime(2152302898747)) # base 5
self.assertFalse(isPrime(3474749660383)) # base 6
self.assertFalse(isPrime(341550071728321)) # base 7
self.assertFalse(isPrime(341550071728321)) # base 8
self.assertFalse(isPrime(3825123056546413051)) # base 9
self.assertFalse(isPrime(3825123056546413051)) # base 10
self.assertFalse(isPrime(3825123056546413051)) # base 11
# Zhang (2007)
self.assertFalse(isPrime(318665857834031151167461)) # base 12
self.assertFalse(isPrime(3317044064679887385961981)) # base 13
# base 14
self.assertFalse(isPrime(6003094289670105800312596501))
# base 15
self.assertFalse(isPrime(59276361075595573263446330101))
# base 16
self.assertFalse(isPrime(564132928021909221014087501701))
# base 17
self.assertFalse(isPrime(564132928021909221014087501701))
# base 18
self.assertFalse(isPrime(1543267864443420616877677640751301))
# base 19
self.assertFalse(isPrime(1543267864443420616877677640751301))
# F. Arnault "Constructing Carmichael Numbers Which Are Strong
# Pseudoprimes to Several Bases". Journal of Symbolic
# Computation. 20 (2): 151-161. doi:10.1006/jsco.1995.1042.
# Section 4.4 Large Example (a pseudoprime to all bases up to
# 300)
p = int("29 674 495 668 685 510 550 154 174 642 905 332 730 "
"771 991 799 853 043 350 995 075 531 276 838 753 171 "
"770 199 594 238 596 428 121 188 033 664 754 218 345 "
"562 493 168 782 883".replace(" ", ""))
self.assertTrue(isPrime(p))
self.assertFalse(p * (313 * (p - 1) + 1) * (353 * (p - 1) + 1))
def test_with_small_composites(self):
self.assertFalse(isPrime(4))
self.assertFalse(isPrime(6))
self.assertFalse(isPrime(9))
self.assertFalse(isPrime(10))
def test_with_small_primes(self):
self.assertTrue(isPrime(3))
self.assertTrue(isPrime(5))
self.assertTrue(isPrime(7))
self.assertTrue(isPrime(11))
def test_getRandomSafePrime(self):
r = getRandomSafePrime(20)
self.assertEqual(numBits(r), 20)
self.assertTrue(isPrime(r))
self.assertTrue(isPrime((r - 1) // 2))
def test_getRangomPrime(self):
r = getRandomPrime(20)
self.assertEqual(numBits(r), 20)
self.assertTrue(isPrime(r))
def test_with_hard_primes_to_test(self):
# XXX Rabin-Miller fails to properly detect following composites
with self.assertRaises(AssertionError):
for i in range(100):
# OEIS A014233
self.assertFalse(isPrime(2047))
self.assertFalse(isPrime(1373653))
self.assertFalse(isPrime(25326001))
self.assertFalse(isPrime(3215031751))
self.assertFalse(isPrime(2152302898747))
self.assertFalse(isPrime(3474749660383))
self.assertFalse(isPrime(341550071728321))
self.assertFalse(isPrime(341550071728321))
self.assertFalse(isPrime(3825123056546413051))
self.assertFalse(isPrime(3825123056546413051))
self.assertFalse(isPrime(3825123056546413051))