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Miller-Rabin primality test (deterministic version) in Python
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''' partly stolen from http://en.literateprograms.org/Miller-Rabin_primality_test_(Python) ''' | |
def miller_rabin_pass(a, s, d, n): | |
a_to_power = pow(a, d, n) | |
if a_to_power == 1: | |
return True | |
for i in xrange(s-1): | |
if a_to_power == n - 1: | |
return True | |
a_to_power = (a_to_power * a_to_power) % n | |
return a_to_power == n - 1 | |
def miller_rabin(n): | |
'''if n < 1,373,653, it is enough to test a = 2 and 3; | |
if n < 9,080,191, it is enough to test a = 31 and 73; | |
if n < 4,759,123,141, it is enough to test a = 2, 7, and 61; | |
if n < 2,152,302,898,747, it is enough to test a = 2, 3, 5, 7, and 11;''' | |
if n < 2: return False | |
if n in {2, 7, 61}: return True | |
d = n - 1 | |
s = 0 | |
while d % 2 == 0: | |
d >>= 1 | |
s += 1 | |
for a in {2,7,61}: | |
if not miller_rabin_pass(a, s, d, n): | |
return False | |
return True |
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no se como lo hicistes, lo vistes o descubistes, pero funciona estupendo