How can I run PRP test?

bbb120 · 2020-11-17, 06:13

Quote:

Originally Posted by engracio

Well guys it was nice while it lasted. Pending on more rigorous testing by Phil, we have BUSTED nummer funf.

I thought I might post this prior to more verification to let others go on to other projects on their queue.

which software can give a PRP test ?
how long does it cost ?

VBCurtis · 2020-11-17, 06:41

LLR, or pfgw. Time taken depends rather heavily on hardware, just like it does for Prime95.
A prp test is about the same speed as what P95 would take on that same size of exponent.

firejuggler · 2020-11-17, 06:43

at this size, primo isn't practical

sweety439 · 2020-11-17, 16:18

Quote:

Originally Posted by firejuggler

at this size, primo isn't practical

Well, primo cannot handle numbers > 2^65536, or the repunit R49081 (=(10^49081-1)/9) will be already proven to be prime.

VBCurtis · 2020-11-17, 16:56

Quote:

Originally Posted by sweety439

Well, primo cannot handle numbers > 2^65536, or the repunit R49081 (=(10^49081-1)/9) will be already proven to be prime.

https://primes.utm.edu/top20/page.php?id=27 suggests you're mistaken about the size of numbers Primo can handle.

Maybe you should run that Primo proof yourself- it's just 25% or so more digits than the current record holder. Shouldn't take you long, right?

carpetpool · 2020-11-17, 21:23

I would happily certify it if I had the resources. Unfortunately for Primo (which can run about 64 concurrent tasks at a time), the time complexity for certifying N prime is at least O(ln(N)^4). I had asked about how long it would take to run some time ago.

In A PM, I was given these averages times for certifying a 25k digit number.

64 cores (22.5 days)
32 cores (45 days)
16 cores (3 months)
8 cores (6 months)
4 cores (1 year)

So for 50k digits, we have

64 cores (360 days) Almost a year!!!
32 cores (720 days)
16 cores (1440 days)
8 cores (2880 days)
4 cores (5760 days)

At best, you could probably certify R49081 in just a little under a year.

Puzzle-Peter · 2020-11-24, 17:03

Primo has a built-in limit on the candidate size. Marcel Martin increases the limit from time to time as better hardware allows for bigger tests. At the moment the limit is 132,928 bits which is about 40,000 decimal digits. So at least for now, no chance. Maybe in a future update it will be possible to certify R49081.

PS: on the other hand that means the next three numbers in the probable primes thread are now within the primo limit but with numbers that close to the theoretical limit there is still a chance of primo being unable to provide a proof.

paulunderwood · 2020-11-24, 17:21

Quote:

Originally Posted by Puzzle-Peter

Maybe in a future update it will be possible to certify R49081.

I have an experimental version of Primo

Puzzle-Peter · 2020-11-25, 14:27

Quote:

Originally Posted by paulunderwood

I have an experimental version of Primo

Cool. I've had my share of XXL certificates. No more...

2020-11-24, 17:03	#7
Puzzle-Peter Jun 2009 1010101011₂ Posts	Primo has a built-in limit on the candidate size. Marcel Martin increases the limit from time to time as better hardware allows for bigger tests. At the moment the limit is 132,928 bits which is about 40,000 decimal digits. So at least for now, no chance. Maybe in a future update it will be possible to certify R49081. PS: on the other hand that means the next three numbers in the probable primes thread are now within the primo limit but with numbers that close to the theoretical limit there is still a chance of primo being unable to provide a proof. Last fiddled with by Puzzle-Peter on 2020-11-24 at 17:17

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2020-11-17, 06:41	#2
VBCurtis "Curtis" Feb 2005 Riverside, CA 2·5·11·43 Posts	LLR, or pfgw. Time taken depends rather heavily on hardware, just like it does for Prime95. A prp test is about the same speed as what P95 would take on that same size of exponent.

2020-11-17, 06:43	#3
firejuggler Apr 2010 Over the rainbow 2³×317 Posts	at this size, primo isn't practical

2020-11-17, 21:23	#6
carpetpool "Sam" Nov 2016 101000110₂ Posts	I would happily certify it if I had the resources. Unfortunately for Primo (which can run about 64 concurrent tasks at a time), the time complexity for certifying N prime is at least O(ln(N)^4). I had asked about how long it would take to run some time ago. In A PM, I was given these averages times for certifying a 25k digit number. 64 cores (22.5 days) 32 cores (45 days) 16 cores (3 months) 8 cores (6 months) 4 cores (1 year) So for 50k digits, we have 64 cores (360 days) Almost a year!!! 32 cores (720 days) 16 cores (1440 days) 8 cores (2880 days) 4 cores (5760 days) At best, you could probably certify R49081 in just a little under a year.