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725834b9bc
* Added binary exponentiaion with respect to modulo * Added miller rabin: the probabilistic primality test for large numbers * Removed unused import * Added test for miller_rabin * Add test to binary_exp_mod * Removed test parameter to make Travis CI happy * unittest.main() # doctest: +ELLIPSIS ... * Update binary_exp_mod.py * Update binary_exp_mod.py * Update miller_rabin.py * from .prime_check import prime_check Co-authored-by: Christian Clauss <cclauss@me.com>
51 lines
1.2 KiB
Python
51 lines
1.2 KiB
Python
import random
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from .binary_exp_mod import bin_exp_mod
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# This is a probabilistic check to test primality, useful for big numbers!
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# if it's a prime, it will return true
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# if it's not a prime, the chance of it returning true is at most 1/4**prec
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def is_prime(n, prec=1000):
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"""
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>>> from .prime_check import prime_check
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>>> all(is_prime(i) == prime_check(i) for i in range(1000))
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True
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"""
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if n < 2:
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return False
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if n % 2 == 0:
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return n == 2
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# this means n is odd
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d = n - 1
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exp = 0
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while d % 2 == 0:
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d /= 2
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exp += 1
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# n - 1=d*(2**exp)
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count = 0
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while count < prec:
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a = random.randint(2, n - 1)
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b = bin_exp_mod(a, d, n)
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if b != 1:
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flag = True
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for i in range(exp):
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if b == n - 1:
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flag = False
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break
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b = b * b
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b %= n
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if flag:
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return False
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count += 1
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return True
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if __name__ == "__main__":
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n = abs(int(input("Enter bound : ").strip()))
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print("Here's the list of primes:")
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print(", ".join(str(i) for i in range(n + 1) if is_prime(i)))
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