The question is about factoring extremely large integers but you can have a look at this question to see the context if it helps. Please note that I am not very familiar with mathematical notation so would appreciate a verbose description of equations.
The integer in question will ALWAYS be a power of N and will be known to us to calculate against. So let's assume N = 2 for example. That will give us a sequence of numbers like:
2, 4, 8, 16... up to hundreds of thousands of digits.
I need to find all possible factors (odd, even, prime, etc.) as efficiently as possible.
What is the solution and how could I understand this from mathematical and computational perspectives?
Does the fact that each number to be factored is a power of 2 help in eliminating any complexity or computational time?