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Write the function is_mersenne that receives a single prime number p and returns True if it is a Mersenne prime, or False otherwise.
Now it's time to find which of the prime numbers in the primes variable are indeed Mersenne primes. Find all Mersenne primes and store them in the variable mersenne_primes. Your list will contain the elements [3, 7, 31, 127, ...].
Create a list of Mersenne numbers from 1 up to the one that is larger than the largest prime in the list of primes. That is, suppose our list of primes contained the first 12 primes: [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]
You should start calculating all integers starting from 1
1 = (2^1) - 1 = 1
2 = (2^2) - 1 = 3
3 = (2^3) - 1 = 7
4 = (2^4) - 1 = 15
5 = (2^5) - 1 = 31
6 = (2^6) - 1 = 63 <<<< 63 is LARGER than the largest prime in our list, which is 37. This is NOT included.
In this case, your list should contain only the mersenne numbers: [1, 3, 7, 15, 31].
We'll use the list mersenne_numbers to check which numbers in primes are Mersenne numbers. So, the ultimate efficient gain will be to turn mersenne_numbers into a set, as the operations of membership in sets are O(1).
Transform the variable mersenne_numbers into a set containing the same elements.
Now, create a new variable efficient_mersenne_primes that contains all the mersenne numbers (same as before), but this time, check if the prime is a mersenne using the set mersenne_numbers created in the previous activity.
