So, recently, I was playing around with random numbers and their prime factorizations in my free time. Basically, what I would do, was take a number, say x.
I would take the prime factorization of x, then add 1 to x, and try comparing the prime factorizations of, both to see if there is a pattern that is present.
Let's assume x to be 24 here:
$24 = 2^3 * 3$
$25 = 5^2$
I can't really seem to find a pattern over here, Aside from the fact that 5 is the sum of 2 and 3. I was wondering if there is some sort of pattern to this specific example, or even better, a sort of pattern to any general example. If not, is it possible to find one? And if the prime factorizations are truly random, is there some way to prove it?
Yours Sincerely, Aster17