I’ve got my own personal sieve for huge numbers, I was able to generate a number larger than the known largest prime number, but I need a certificate for the prime, and PrimeQ is taking more than one day to give me an answer.
Can I send to someplace at Wolfram to get it verified?
According to
- https://mathematica.stackexchange.com/questions/132670/some-information-about-primeq-function
- https://math.stackexchange.com/questions/123465/do-we-really-know-the-reliability-of-primeqn-for-n1016
the test used in PrimeQ is not necessarily accurate above 2^{64}. I’d be curious to hear from someone at Wolfram about if implementation details have changed.
I suppose you might resort to the PPP, Primality Proving Package—Wolfram Documentation. I have no experience with this though.
Hi there, thank you so much for your answer even though it was not what I wished …but hey some questions really have no answer…thank you.
Implementation details will change with the next release, to use an updated version of the Baiillie-PSW method.
This of course remains probabilistic. Here is Robert Baillie’s remark though, which strikes me as quite apt for the problem at hand. “There are zero known counterexamples to the original BPSW, and we expect the new test to have even fewer :)”
Thank you Dr. Daniel looking forward to it… i will read the article you send me…thank you so much!!!
So was updated PSW implemented?
Yes, PrimeQ uses the recent version of PSW.
So base 3 Miller-Rabin no longer is used, THAT is great. BTW, you did not forget gcd(Q, n) == 1 check, right? See other implementation: Add a GCD check to the Lucas test by fjarri · Pull Request #11 · entropyxyz/crypto-primes · GitHub
As best I can tell, the Miller-Rabin 3-psuedoprime test is not used.
Regarding our current Lucas test, I believe the reference implementation I posted on Community is equivalent to what is implemented in our internal code.