Mersenne Prime is a prime number that is one less than a power of two. In other words, any prime is Mersenne Prime if it is of the form 2k-1 where k is an integer greater than or equal to 2. First few Mersenne Primes are 3, 7, 31 and 127.
The task is to find all Mersenne Primes smaller than equal to an input positive integer n.
Input: n = 10 Output: 3 7 Explanation:3 and 7 are only prime numbers which are less than equal to 10 and in the form of 2k - 1.
Input: n = 100 Output: 3 7 31 Explanation: 3, 7 and 31 are only prime numbers which are less than equal to 100 and in the form of 2k - 1.
You don't need to read or print anything. Your task is to complete the function AllMersennePrimeNo() which takes n as input parameter and returns a list of all Mersenne Primes less than or equal to n in sorted order.
Expected Time Complexity: O(n * log(log(n))
Expected Space Complexity: O(n)
1 <= n <= 100000
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