How can I run PRP test?
 

[QUOTE=engracio;251897]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.:smile:[/QUOTE]

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

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.

at this size, primo isn't practical

[QUOTE=firejuggler;563457]at this size, primo isn't practical[/QUOTE]

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

[QUOTE=sweety439;563507]Well, primo cannot handle numbers > 2^65536, or the repunit R49081 (=(10^49081-1)/9) will be already proven to be prime.[/QUOTE]

[url]https://primes.utm.edu/top20/page.php?id=27[/url] 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?

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.

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.

[QUOTE=Puzzle-Peter;564219]Maybe in a future update it will be possible to certify R49081.
[/QUOTE]

I have an experimental version of Primo :devil:

[QUOTE=paulunderwood;564224]I have an experimental version of Primo :devil:[/QUOTE]


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