python - Find Mersenne prime numbers using list comprehensions and my code

Question

I wrote this code to find prime numbers, but how could I change it to find Mersenne prime numbers?

def prime_test_list(n,known_primes):
k = 1
stop_val = len(known_primes)
if(n>2):
    while k<stop_val:
        cprime = known_primes[k]
        if n%cprime == 0:
            return 0            
        else:
            k+=1
    return 1
else:
    return 1

def prime_print_list(a):
    n = 2
    known_primes = [1] 
    while(n<a):
        val = prime_test_list(n,known_primes)
        if(val==1):
            known_primes.append(n)            
        n+=1
    print known_primes

Answer 1

Something like this:

def mersenne_test(n):

    k = 0
    m = 0
    while m<=n:
        m = 2**k-1
        if(n==m):
            return "This number is a Mersenne number since it is equal by to 2**%d-1" % k
        k += 1
    return "This number is not a Mersenne number."