>>12732642yeah, not OP.
I hop in threads like this because I studied and practiced some number theory and it's fun to post about related topics. I hopped in this one specifically because the time complexity mention.
Time complexity is not my specialty, and I've tried to apply it to the work I have, but I'm afraid I'm still a bit off in my understanding of it. Still it's of interest, so I was hoping to learn more.
I did crack some things and created new fomulas and understandings when it comes to integer factorization, the prime distribution, the nth prime, primes of any size, prime checks, and some related topics.
However what I have isn't more efficient than things that already exist, it's just more automatic and concise in some ways symbolically, and implicitly, and could open up the avenue to other understandings and techniques. It gives people a new place from which to work.
I read a bunch more about complexity last night, and I'm still not sure what complexity my functions are running in. Part of what i read about the complexity of brute force would suggest to me my functions are not in polynomial time, however what I've read about the concepts of big O notation would suggest they are, so my understanding is incomplete.
So can they factor any number, yes. Can they give you a prime of any size, sure. Are they faster than brute force, or can be made to be, questionable. But they offer a bunch of choices to be tweaked or adapted, as they are based on a criteria of functions,not an absolute function; so anyone who picks functions meeting a base criteria can apply the method, and hence maybe someone can find a base function that then drastically simplifies they whole process. I've come up with at least 6 base functions that work, all of which then end in different complexities.
Either way, they still provide some techniques that didn't exist before, and answer some unanswered questions. I'd love to find some people in person to discuss them with.
