for example, "31 = 25 − 1", and 5 is a prime number, so 31 is a mersenne number; and 31 is also a mersenne prime because it is a prime number. but the mersenne number "2047 = 211 − 1" is not a prime because it is divisible by 89 and 23. and "24 − 1 = 15" can be shown to be composite because 4 is not prime.