79 lines
2.1 KiB
Python
79 lines
2.1 KiB
Python
import random
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_mrpt_num_trials = 5 # number of bases to test
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def is_probable_prime(n):
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"""
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Miller-Rabin primality test.
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A return value of False means n is certainly not prime. A return value of
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True means n is very likely a prime.
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>>> is_probable_prime(1)
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Traceback (most recent call last):
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...
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AssertionError
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>>> is_probable_prime(2)
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True
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>>> is_probable_prime(3)
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True
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>>> is_probable_prime(4)
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False
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>>> is_probable_prime(5)
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True
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>>> is_probable_prime(123456789)
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False
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>>> primes_under_1000 = [i for i in range(2, 1000) if is_probable_prime(i)]
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>>> len(primes_under_1000)
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168
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>>> primes_under_1000[-10:]
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[937, 941, 947, 953, 967, 971, 977, 983, 991, 997]
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>>> is_probable_prime(6438080068035544392301298549614926991513861075340134\
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3291807343952413826484237063006136971539473913409092293733259038472039\
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7133335969549256322620979036686633213903952966175107096769180017646161\
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851573147596390153)
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True
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>>> is_probable_prime(7438080068035544392301298549614926991513861075340134\
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3291807343952413826484237063006136971539473913409092293733259038472039\
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7133335969549256322620979036686633213903952966175107096769180017646161\
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851573147596390153)
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False
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"""
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assert n >= 2
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# special case 2
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if n == 2:
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return True
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# ensure n is odd
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if n % 2 == 0:
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return False
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# write n-1 as 2**s * d
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# repeatedly try to divide n-1 by 2
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s = 0
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d = n-1
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while True:
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quotient, remainder = divmod(d, 2)
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if remainder == 1:
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break
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s += 1
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d = quotient
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assert(2**s * d == n-1)
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# test the base a to see whether it is a witness for the compositeness of n
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def try_composite(a):
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if pow(a, d, n) == 1:
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return False
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for i in range(s):
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if pow(a, 2**i * d, n) == n-1:
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return False
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return True # n is definitely composite
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for i in range(_mrpt_num_trials):
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a = random.randrange(2, n)
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if try_composite(a):
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return False
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return True # no base tested showed n as composite
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