"""⏎
        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 i 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))⏎