erlang-prime-sieve
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videlalvaro
If you have seen this method before, please let me know by opening an issue.
If you have seen this method before, please let me know by opening an issue.
Your method is "For any A005097, multiplied by 2 and then adding 1 to the result will give you a prime number."
The name of the sequence you refer to is "(Odd primes - 1)/2". This suggests that this method of finding primes is known.
Alternative representations of your formula are in the formula section. Kohen's "around a table" representation is identical to yours.
Citations on the sequence go back to 2005. Given that it's math we're talking about, that probably means this was discovered in the 1930s.
Having a sequence doesn't mean having a formula for it. There are many sequences on that website that are known, but that have no formula for it.
Also there might be alternative ways of finding those "A005097" numbers. What I haven't seen is a way using these modulo properties. I've also read that paper by Kohen.
It is possible that I'm misunderstanding. However, counting around a round table starting from the king seems to express modulus properties.
Yep, I will examine this with more detail. I just wanted to get it out here and receive some feedback. As I said on the README I don't think this is ground breaking or anything, maybe two reasons why I thought it was interesting to share were:
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I haven't seen it on Number Theory books, Group Theory books or online (ie wikipedia and so on).
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I've found this by testing some properties of some permutation groups. So I was literally looking into a completely different direction until I saw these pattern of numbers pairs like (N, (N-1)/2) appearing over and over. That's where I've got [(3,1), (5,2), (7,3) ... (N, (N-1)/2)] and son on, in order to discard possible numbers that could give you a prime when multiplied by 2 and then adding 1.
Also, this is not even an optimal sieving method. For me it's just a curiosity.
It's fun. I've also pushed number sieves for fun. I only opened the issue because it seemed to be requested. :)
:+1: