## RE: [PrimeNumbers] Some Benchmark Primality Test

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• Try (00:25:59) gp ispseudoprime(31838235*2^29717+1) %129 = 1 (00:33:39) gp ## *** last result computed in 6mn, 29,015 ms. (17:33:32) gp
Message 1 of 5 , Sep 1, 2009
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Try
(00:25:59) gp > ispseudoprime(31838235*2^29717+1)
%129 = 1
(00:33:39) gp > ##
*** last result computed in 6mn, 29,015 ms.

(17:33:32) gp > isprime(31838235*2^29717+1)
%74 = 1
(18:35:16) gp > ##
*** last result computed in 51mn, 53,938 ms.

c:\pfgw>pfgw -tc -q31838235*2^^29717+1
PFGW Version 20090725.Win_Dev (Beta 'caveat utilitor') [GWNUM 25.12]

Primality testing 31838235*2^29717+1 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Running N-1 test using base 23
Running N+1 test using discriminant 31, base 10+sqrt(31)
Calling N-1 BLS with factored part 100.00% and helper 0.07% (300.08% proof)
31838235*2^29717+1 is prime! (15.3991s+0.0311s)

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

So before you do primo, do pfgw -tc

pfgw ROCKS!

Cino

From: calimero22@...
Date: Mon, 31 Aug 2009 20:05:01 +0000
Subject: [PrimeNumbers] Some Benchmark Primality Test

I post some time test for a primality or pseudoprimality check.

Tests on AMD Sempron 3000+ (1800 Mhz) WIndows XP
n=31838235*2^29717+1 digits: 8954
Tests run by GIOVANNI DI MARIA - email: calimero22@...
Tests give at least a Pseudoprimality PRP.

===================================================================
GMP Library
mpz_probab_prime_p(n,r) r=1 = 72 secs.
mpz_probab_prime_p(n,r) r=0 = 34 secs.
fermat (mpz_powm(2,n,n) = 2^n MOD n = 34 secs.
My implementation Fermat algorytm = 33 secs.
===================================================================
PFGW
pfgw 3.2.2 (On AMD 1800 Mhz) = 3.1 secs.
pfgw 3.2.2 (On INTEL P4 1800 Mhz) = 1.7 secs. <-----
===================================================================
MATHEMATICA
Mathematica PowerMod[2,n,n] (Fermat) = 38 secs.
PrimeQ[n] = 157 secs.
===================================================================
PARI/GP
ispseudoprime(n) BPSW test = 130 secs.
ispseudoprime(n,1) strong Rabin-Miller test for 1 base = 43 secs.
powermod(x,k,m)=lift(Mod(x,m)^k) --> powermod(2,n,n) = 42 secs.
isprime(n) = too long
===================================================================
PROTH.EXE
Normal Test = 5 secs.
===================================================================
LLR.EXE
Normal Test = 7 secs.
===================================================================
PRP.EXE
Normal Test = 7 secs.
===================================================================
PrimeForm.EXE
Normal Test = 24 secs.
===================================================================

[Non-text portions of this message have been removed]
• ... OK ... Using ECPP to re-prove a prime already proven by BLS would be an exercise in fatuity. David
Message 2 of 5 , Sep 1, 2009
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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
• 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 3 of 5 , Sep 1, 2009
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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 4 of 5 , Sep 1, 2009
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