about prime number generation

Garcia Moreno-Esteva, Enrique enrique.garciamoreno-esteva at helsinki.fi
Thu May 19 20:59:45 CEST 2022

Hi Adrien,

Thank you for writing.  Yes, I have looked into it. It is not that fast once you get to really larger numbers, say past 10^10. I have put this project on hold, since I was also working with another math project involving prime numbers which is going much better.  But I will return to it, perhaps in a month or two.


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From: Adrien Prost-Boucle <adrien.prost-boucle at laposte.net>
Sent: Thursday, May 19, 2022 9:39:48 PM
To: Garcia Moreno-Esteva, Enrique <enrique.garciamoreno-esteva at helsinki.fi>; gmp-discuss at gmplib.org <gmp-discuss at gmplib.org>
Subject: Re: about prime number generation

Hi Enrique,

As far as I know, GMP does not at the moment implement what you are looking for.
The best I know is the following (has already been mentioned a bit in the past in this mailing list) :

Curiosity question :
Did you already experiment with the project above, would there be a property of it that makes you want to look elsewhere too ?


On Sat, 2022-04-30 at 12:31 +0000, Garcia Moreno-Esteva, Enrique wrote:
> Hello,
> I apologize this is not a comment about your webpage, but more a question about your library. Would your library contain a function (call it p(n) ) that generates the n-th prime? If it does not, alternatively, do you have a lower bound for  certifiably producing the next prime with the nextprime function in your library (it is probabilistic, but such probabilistic methods are deterministic below certain bounds, so my question is, what is the lower bound for your function)?
> I thank you in advance for your help.
> Enrique Garcia Moreno-Esteva
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