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I may found a new way to find prime numbers (I haven't found anything similar to my method after lots of searching on the internet). I've been able to use it successfully on digits up to 20 digits long but I don't know where to go from here. I know that with so many people interested in this topic that odds are I haven't actually found anything new or special but I'm still cautious about just plastering it on the internet for anyone to see. What's the best course of action? Should I try going to a nearby university or just risk putting it out there and getting feedback?

Edit: it's a primality test

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    $\begingroup$ Well, at some point you'll have to show it to somebody for verification and analysis. If the method is very long and complex you might find it hard to find someone to go through it properly, though perhaps you could summarize the idea(s) involved well enough to get an initial read on it. $\endgroup$ – lulu Jun 1 '17 at 13:23
  • $\begingroup$ Publish it, or put it on some online platform (arXiv and friends). You are indeed right about the number of different techniques to find primes. However, it also happens to pros to do something already done, so even if someone already did your work, it is not a big deal. And it was probably done in a different manner as well. $\endgroup$ – Vincent Jun 1 '17 at 13:23
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    $\begingroup$ Putting it here gives public record of the finding, in case you would like to prove it was you. $\endgroup$ – Kaynex Jun 1 '17 at 13:44
  • $\begingroup$ Doesn't arXiv require you to be endorsed by an institution or something similar? And I guess that's true, I could just post it here $\endgroup$ – Samantha Clark Jun 1 '17 at 13:49
  • $\begingroup$ It's not clear to me from your text, so make sure to distinguish whether your method is primality testing (e.g. trial division, wheel-optimized trial division, Fermat, Euler, Miller-Rabin, BPSW, APR-CL, ECPP) or generating primes (e.g. segmented Sieve of Eratosthenes). Each are useful but they're somewhat different. $\endgroup$ – DanaJ Jun 1 '17 at 16:18
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If you want to check how useful your method is, you could try to estimate the time complexity (https://en.wikipedia.org/wiki/Time_complexity) of your method.

If your method is faster then existing methods (see e.g. https://en.wikipedia.org/wiki/Generating_primes), it may be interesting.

Note that estimating time complexities is sometimes hard, so that only makes sense if you already know about this, or are very determined.

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  • $\begingroup$ I'm not quite sure how I can figure out the time complexity of this method since it varies a lot but just taking a random example. It took 17 steps to determine that 2671956829859281 is definitely not a prime number, I think that's much shorter than other methods. I'm only in highschool too so I have no clue about how to determine time complexity anyway, guess I have some more reading to do :) $\endgroup$ – Samantha Clark Jun 5 '17 at 2:15
  • $\begingroup$ 17 steps indeed sounds very fast. But time complexity is based on asymptotic behavior, not on the behavior on a specific input. If you read up on time complexity, the worst that can happen is that you learn about time complexity ;) $\endgroup$ – Peter Jun 5 '17 at 8:47
  • $\begingroup$ After looking up some stuff about time complexity I'm lead to believe it depends on the number of loops in a program and how many times the loops runs. This means I'll have to look into understanding the math behind my program a bit more since there is only one loop but the number of times it has to run varies. For example testing 9 the loops runs twice, for 10 it runs once, for 11 it runs once, for 12 it runs twice, etc. There are a few patterns I've noticed but it's still mostly a mystery for me how I can predict the number of times the loops has to run. I'll update once I figure it out $\endgroup$ – Samantha Clark Jun 5 '17 at 13:56

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