160 lines
6.9 KiB
Python
160 lines
6.9 KiB
Python
from sympy.ntheory.generate import Sieve, sieve
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from sympy.ntheory.primetest import (mr, is_lucas_prp, is_square,
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is_strong_lucas_prp, is_extra_strong_lucas_prp, isprime, is_euler_pseudoprime,
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is_gaussian_prime)
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from sympy.testing.pytest import slow
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from sympy.core.numbers import I
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def test_euler_pseudoprimes():
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assert is_euler_pseudoprime(9, 1) == True
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assert is_euler_pseudoprime(341, 2) == False
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assert is_euler_pseudoprime(121, 3) == True
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assert is_euler_pseudoprime(341, 4) == True
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assert is_euler_pseudoprime(217, 5) == False
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assert is_euler_pseudoprime(185, 6) == False
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assert is_euler_pseudoprime(55, 111) == True
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assert is_euler_pseudoprime(115, 114) == True
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assert is_euler_pseudoprime(49, 117) == True
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assert is_euler_pseudoprime(85, 84) == True
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assert is_euler_pseudoprime(87, 88) == True
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assert is_euler_pseudoprime(49, 128) == True
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assert is_euler_pseudoprime(39, 77) == True
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assert is_euler_pseudoprime(9881, 30) == True
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assert is_euler_pseudoprime(8841, 29) == False
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assert is_euler_pseudoprime(8421, 29) == False
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assert is_euler_pseudoprime(9997, 19) == True
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def test_is_extra_strong_lucas_prp():
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assert is_extra_strong_lucas_prp(4) == False
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assert is_extra_strong_lucas_prp(989) == True
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assert is_extra_strong_lucas_prp(10877) == True
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assert is_extra_strong_lucas_prp(9) == False
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assert is_extra_strong_lucas_prp(16) == False
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assert is_extra_strong_lucas_prp(169) == False
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@slow
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def test_prps():
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oddcomposites = [n for n in range(1, 10**5) if
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n % 2 and not isprime(n)]
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# A checksum would be better.
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assert sum(oddcomposites) == 2045603465
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assert [n for n in oddcomposites if mr(n, [2])] == [
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2047, 3277, 4033, 4681, 8321, 15841, 29341, 42799, 49141,
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52633, 65281, 74665, 80581, 85489, 88357, 90751]
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assert [n for n in oddcomposites if mr(n, [3])] == [
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121, 703, 1891, 3281, 8401, 8911, 10585, 12403, 16531,
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18721, 19345, 23521, 31621, 44287, 47197, 55969, 63139,
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74593, 79003, 82513, 87913, 88573, 97567]
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assert [n for n in oddcomposites if mr(n, [325])] == [
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9, 25, 27, 49, 65, 81, 325, 341, 343, 697, 1141, 2059,
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2149, 3097, 3537, 4033, 4681, 4941, 5833, 6517, 7987, 8911,
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12403, 12913, 15043, 16021, 20017, 22261, 23221, 24649,
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24929, 31841, 35371, 38503, 43213, 44173, 47197, 50041,
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55909, 56033, 58969, 59089, 61337, 65441, 68823, 72641,
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76793, 78409, 85879]
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assert not any(mr(n, [9345883071009581737]) for n in oddcomposites)
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assert [n for n in oddcomposites if is_lucas_prp(n)] == [
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323, 377, 1159, 1829, 3827, 5459, 5777, 9071, 9179, 10877,
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11419, 11663, 13919, 14839, 16109, 16211, 18407, 18971,
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19043, 22499, 23407, 24569, 25199, 25877, 26069, 27323,
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32759, 34943, 35207, 39059, 39203, 39689, 40309, 44099,
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46979, 47879, 50183, 51983, 53663, 56279, 58519, 60377,
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63881, 69509, 72389, 73919, 75077, 77219, 79547, 79799,
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82983, 84419, 86063, 90287, 94667, 97019, 97439]
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assert [n for n in oddcomposites if is_strong_lucas_prp(n)] == [
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5459, 5777, 10877, 16109, 18971, 22499, 24569, 25199, 40309,
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58519, 75077, 97439]
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assert [n for n in oddcomposites if is_extra_strong_lucas_prp(n)
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] == [
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989, 3239, 5777, 10877, 27971, 29681, 30739, 31631, 39059,
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72389, 73919, 75077]
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def test_isprime():
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s = Sieve()
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s.extend(100000)
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ps = set(s.primerange(2, 100001))
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for n in range(100001):
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# if (n in ps) != isprime(n): print n
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assert (n in ps) == isprime(n)
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assert isprime(179424673)
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assert isprime(20678048681)
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assert isprime(1968188556461)
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assert isprime(2614941710599)
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assert isprime(65635624165761929287)
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assert isprime(1162566711635022452267983)
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assert isprime(77123077103005189615466924501)
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assert isprime(3991617775553178702574451996736229)
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assert isprime(273952953553395851092382714516720001799)
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assert isprime(int('''
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531137992816767098689588206552468627329593117727031923199444138200403\
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559860852242739162502265229285668889329486246501015346579337652707239\
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409519978766587351943831270835393219031728127'''))
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# Some Mersenne primes
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assert isprime(2**61 - 1)
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assert isprime(2**89 - 1)
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assert isprime(2**607 - 1)
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# (but not all Mersenne's are primes
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assert not isprime(2**601 - 1)
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# pseudoprimes
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#-------------
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# to some small bases
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assert not isprime(2152302898747)
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assert not isprime(3474749660383)
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assert not isprime(341550071728321)
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assert not isprime(3825123056546413051)
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# passes the base set [2, 3, 7, 61, 24251]
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assert not isprime(9188353522314541)
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# large examples
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assert not isprime(877777777777777777777777)
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# conjectured psi_12 given at http://mathworld.wolfram.com/StrongPseudoprime.html
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assert not isprime(318665857834031151167461)
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# conjectured psi_17 given at http://mathworld.wolfram.com/StrongPseudoprime.html
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assert not isprime(564132928021909221014087501701)
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# Arnault's 1993 number; a factor of it is
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# 400958216639499605418306452084546853005188166041132508774506\
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# 204738003217070119624271622319159721973358216316508535816696\
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# 9145233813917169287527980445796800452592031836601
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assert not isprime(int('''
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803837457453639491257079614341942108138837688287558145837488917522297\
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427376533365218650233616396004545791504202360320876656996676098728404\
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396540823292873879185086916685732826776177102938969773947016708230428\
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687109997439976544144845341155872450633409279022275296229414984230688\
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1685404326457534018329786111298960644845216191652872597534901'''))
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# Arnault's 1995 number; can be factored as
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# p1*(313*(p1 - 1) + 1)*(353*(p1 - 1) + 1) where p1 is
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# 296744956686855105501541746429053327307719917998530433509950\
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# 755312768387531717701995942385964281211880336647542183455624\
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# 93168782883
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assert not isprime(int('''
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288714823805077121267142959713039399197760945927972270092651602419743\
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230379915273311632898314463922594197780311092934965557841894944174093\
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380561511397999942154241693397290542371100275104208013496673175515285\
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922696291677532547504444585610194940420003990443211677661994962953925\
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045269871932907037356403227370127845389912612030924484149472897688540\
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6024976768122077071687938121709811322297802059565867'''))
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sieve.extend(3000)
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assert isprime(2819)
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assert not isprime(2931)
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assert not isprime(2.0)
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def test_is_square():
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assert [i for i in range(25) if is_square(i)] == [0, 1, 4, 9, 16]
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# issue #17044
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assert not is_square(60 ** 3)
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assert not is_square(60 ** 5)
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assert not is_square(84 ** 7)
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assert not is_square(105 ** 9)
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assert not is_square(120 ** 3)
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def test_is_gaussianprime():
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assert is_gaussian_prime(7*I)
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assert is_gaussian_prime(7)
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assert is_gaussian_prime(2 + 3*I)
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assert not is_gaussian_prime(2 + 2*I)
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