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861a8c3631
* Add Lucas_Lehmer_primality_test * Add explanation for Lucas_Lehmer_primality_test * Update and rename Lucas_Lehmer_primality_test.py to lucas_lehmer_primality_test.py
43 lines
1.1 KiB
Python
43 lines
1.1 KiB
Python
# -*- coding: utf-8 -*-
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"""
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In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers.
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https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test
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A Mersenne number is a number that is one less than a power of two.
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That is M_p = 2^p - 1
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https://en.wikipedia.org/wiki/Mersenne_prime
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The Lucas–Lehmer test is the primality test used by the
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Great Internet Mersenne Prime Search (GIMPS) to locate large primes.
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"""
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# Primality test 2^p - 1
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# Return true if 2^p - 1 is prime
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def lucas_lehmer_test(p: int) -> bool:
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"""
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>>> lucas_lehmer_test(p=7)
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True
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>>> lucas_lehmer_test(p=11)
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False
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# M_11 = 2^11 - 1 = 2047 = 23 * 89
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"""
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if p < 2:
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raise ValueError("p should not be less than 2!")
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elif p == 2:
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return True
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s = 4
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M = (1 << p) - 1
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for i in range(p - 2):
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s = ((s * s) - 2) % M
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return s == 0
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if __name__ == "__main__":
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print(lucas_lehmer_test(7))
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print(lucas_lehmer_test(11))
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