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How big a number can PrimeQ work?

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?
POSTED BY: Luis Felipe Massena Misiec
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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.
POSTED BY: Luis Felipe Massena Misiec
POSTED BY: Adam Mendenhall
POSTED BY: Daniel Lichtblau

Thank you Dr. Daniel looking forward to it... i will read the article you send me...thank you so much!!!
POSTED BY: Luis Felipe Massena Misiec
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Posted 2 years ago

So was updated PSW implemented?
POSTED BY: ZAQU zaqu

Yes, PrimeQ uses the recent version of PSW.
POSTED BY: Daniel Lichtblau
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ZAQU zaqu
Posted 2 years ago
POSTED BY: ZAQU zaqu

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.
POSTED BY: Daniel Lichtblau
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