A [Mersenne prime](https://en.wikipedia.org/wiki/Mersenne_prime) is a prime number that can be represented as:
Mn = 2^(n) - 1. Therefore, every Mersenne prime is one less than a power of two. 

Write a function that will return whether the given integer `n` will produce a Mersenne prime or not.

The tests will check random integers up to 2000.

Difficulty: EASY
Starter code: def valid_mersenne(n):
	

Solutions:
def valid_mersenne(n):
	return n in {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279}


def valid_mersenne(n):
	if n < 2:
		return False
	if n == 2:
		return True
	mersenne = 2 ** n - 1
	residue = 4
	for _ in range(n - 2):
		residue = (residue * residue - 2) % mersenne
	return not residue


def valid_mersenne(n):
	return n == 2 or (is_prime(n) and lucas_lehmer(n))

def is_prime(n):
	from itertools import chain
	return all((n % i != 0 for i in chain([2], range(3, int(n ** 0.5) + 1, 2))))

def lucas_lehmer(n):
	s = 4
	M = 2 ** n - 1
	for _ in range(n - 2):
		s = (s * s - 2) % M
	return s == 0


A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609}

def valid_mersenne(n):
	return n in A000043


def valid_mersenne(n):
	return n in [2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941]


valid_mersenne = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279}.__contains__