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## RE: [PrimeNumbers] Re: Some Benchmark Primality Test

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• Hi David, ... anayway, I thought we were benchmarking in this last post? I am still curious how long it would take primo to prove 31838235*2^29717+1 is prime.
Message 1 of 5 , Sep 1, 2009
Hi David,

>So before you do primo, do pfgw -tc

anayway, I thought we were benchmarking in this last post?

I am still curious how long it would take primo to prove 31838235*2^29717+1 is prime.

At fiirst, I thought time was proportional to the number of digits but now I realize
that ain't so. "When in doubt, specialize"

Not all lost though. I learned a new word.

I tried pfgw on the primo top entry of the top 20.

http://www.ellipsa.eu/public/primo/top20.html

c:\pfgw>pfgw -tc -q2^^29727+20273
PFGW Version 20090725.Win_Dev (Beta 'caveat utilitor') [GWNUM 25.12]

Primality testing 2^29727+20273 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 9+sqrt(19)
Calling N+1 BLS with factored part 0.08% and helper 0.07% (0.30% proof)
2^29727+20273 is Fermat and Lucas PRP! (12.4107s+0.0008s)

Interesting.

What dominion does 31838235*2^29717+1 have over 1*2^29727+20273?

Is 80 days the best that can be done for the top primo prime?

http://primes.utm.edu/primes/page.php?id=89447

pfgw still ROCKS!

Cino

Date: Tue, 1 Sep 2009 22:24:24 +0000
Subject: [PrimeNumbers] Re: Some Benchmark Primality Test

cino hilliard <hillcino368@...> wrote:

> 31838235*2^29717+1 is prime! (15.3991s+0.0311s)

OK

> This 8954 digit number will be the top primo candidate
> if you have the time

Using ECPP to re-prove a prime already proven by BLS
would be an exercise in fatuity.

David

[Non-text portions of this message have been removed]
• ... Very roughly, I reckon that the Primo time is proportional to digits^(9/2). David
Message 2 of 5 , Sep 1, 2009