# asweigart/codebreaker

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 # Primality Testing with the Rabin-Miller Algorithm # http://inventwithpython.com/codebreaker (BSD Licensed) import random def main(): print('Example prime testing:') for num in (2, 3, 5, 10, 100, 101, 5099806053, 5099806057): print('%s is prime: %s' % (num, isPrime(num))) def rabinMiller(num): # Returns True if num is a prime number. s = num - 1 t = 0 while s % 2 == 0: # keep halving s until it is even (and use t # to count how many times we halve s) s = s // 2 t += 1 for dummy_trials in range(5): # try to falsify num's primality 5 times a = random.randrange(2, num - 1) v = pow(a, s, num) if v != 1: # this test does not apply if v is 1. i = 0 while v != (num - 1): if i == t - 1: return False else: i = i + 1 v = (v ** 2) % num return True def isPrime(num): # Return True if num is a prime number. This function does a quicker # prime number check before calling rabinMiller(). # About a 1/3 of the time we can quickly determine if num is not prime # by dividing by the first few dozen prime numbers. This is quicker # than rabinMiller(), but unlike rabinMiller() is not guaranteed to # prove that a number is prime. lowPrimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997] if (num < 2): return False if num in lowPrimes: return True # See if any of the low prime numbers can divide num for prime in lowPrimes: if (num % prime == 0): return False # If all else fails, call rabinMiller() to determine if num is a prime. return rabinMiller(num) def generateLargePrime(keysize=1024): # Return a random prime number of keysize bits in size. while True: n = random.randrange(2**(keysize-1), 2**(keysize)) if isPrime(n) == True: return n if __name__ == '__main__': main()
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