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Python implementation of the Miller-Rabin Primality Test
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def miller_rabin(n, k): | |
# Implementation uses the Miller-Rabin Primality Test | |
# The optimal number of rounds for this test is 40 | |
# See http://stackoverflow.com/questions/6325576/how-many-iterations-of-rabin-miller-should-i-use-for-cryptographic-safe-primes | |
# for justification | |
# If number is even, it's a composite number | |
if n == 2: | |
return True | |
if n % 2 == 0: | |
return False | |
r, s = 0, n - 1 | |
while s % 2 == 0: | |
r += 1 | |
s //= 2 | |
for _ in xrange(k): | |
a = random.randrange(2, n - 1) | |
x = pow(a, s, n) | |
if x == 1 or x == n - 1: | |
continue | |
for _ in xrange(r - 1): | |
x = pow(x, 2, n) | |
if x == n - 1: | |
break | |
else: | |
return False | |
return True |
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