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