The probable primes

[Puzzle-Peter]

Done. I'll upload the certificate to factordb.

http://primes.utm.edu/primes/page.php?id=118567

[philmoore]

Very nice, congratulations, Peter! Congratulations as well to Marcel for some very impressive improvements to Primo. This number is now the eighth largest ECPP, Peter's result from last December which was then the third largest is now the seventh, and Primo has now proven 6 out of the 8 top ECPP results, including the second largest, which is also the largest proven Wagstaff prime.

The next three probable primes on the list (see post #1 in this thread) have 31237, 31336, and 31846 digits respectively, and are considerably larger than the current ECPP record of 26643 digits. Probably too soon to tackle these yet, but I expect they will be proven in a few years. If anyone checks to see how the current version of Primo does on any of these, a report would be welcome.

[Puzzle-Peter]

Originally Posted by philmoore

If anyone checks to see how the current version of Primo does on any of these, a report would be welcome.

According to Marcel Martin, the theoretical limit that PRIMO can handle is a little bit less than 100,000 bits, so no chance of doing these plus he told me he does not plan on extending PRIMOs limit.

EDIT: found his mail, the limit is 99648 bits

[danaj]

Congrats!

When I started my P18689 in Sep 2013, it would have been the largest Primo result. It took 3 months with Primo 4.0.1 + 4.0.4 on a 3930K (12 threads, which is faster on that machine than 6 -- perhaps faster memory), and ended up 2nd behind Peter when it finished, and is now 11th. That's my main dev machine so ran lots of xterms plus a few other programs at the same time though nothing very long running. I also had a fun scare a couple months in when another process filled the disk and Primo crashed, losing all the data. Daily backups to the rescue.

[Puzzle-Peter]

LOL I know that feeling! Had the "no space left on device" problem after about 1500 tests. PRIMO crunched on, but the files had 0 bytes. Then, in phase 2, the next shock. Every test needs 3 steps in phase 2 "building polynomial", "factoring polynomial" and "computing curve and point". I never noticed the first one, because it takes so little time. But one test spent more than 10 hours on "building polynomial". I thought it had crashed or maybe the intermediate file was corrupt. But on the next morning it had moved on...

This is most probably the end of my XXL PRIMO test series. Let's wait for Paul to finish his monster and then let's see what will happen.

[henryzz]

Is there a particular reason why the latest versions of fastecpp are not available?

[philmoore]

Originally Posted by Puzzle-Peter

According to Marcel Martin, the theoretical limit that PRIMO can handle is a little bit less than 100,000 bits, so no chance of doing these plus he told me he does not plan on extending PRIMOs limit.

EDIT: found his mail, the limit is 99648 bits

Now that Primo has proven a new ECPP record at 29271 digits, our next three numbers (31237 to 31846 digits) don't seem that far from possible. It will be interesting to see how long the new record stands. The current Primo limit is 29998 digits, so the program has now worked successfully close to this limit.

[Puzzle-Peter]

Originally Posted by philmoore

Now that Primo has proven a new ECPP record at 29271 digits, our next three numbers (31237 to 31846 digits) don't seem that far from possible. It will be interesting to see how long the new record stands. The current Primo limit is 29998 digits, so the program has now worked successfully close to this limit.

AFAIK the next release (due in Jan.) will be able to do up to ~35000 digits.

[XYYXF]

Any reservations for ECPP?

[ET_]

Originally Posted by bbb120

You can use mathematica ,function PrimeQ[2^73360+10711]

MillerRabin[n0_,a0_]:=Module[{n=n0,a=a0,s,m,t1,k},
    s=0;m=n-1;While[Mod[m,2]==0,m=m/2;s=s+1];
    t1=PowerMod[a,m,n];
    If[t1==1,Return[True]];
    k=0;While[k<s-1&&t1!=n-1,k=k+1;t1=Mod[t1^2,n]];
    If[t1==n-1,Return[True],Return[False]]
]

Miller Rabin code by using mathematica,

MillerRabin[2^73360+10711, #] & /@ {17, 257, 65537, 10^200 + 267}
{True, True, True, True}
this is too fast,ECPP is too slow,

miller rabin is simple and realible!

Miller-Rabin does not certificate a prime, it shows PRPs.

[bbb120]

Originally Posted by ET_

Miller-Rabin does not certificate a prime, it shows PRPs.

miller rabin really does not give any certificate a prime ,
but several miller rabin test with one lucas test is very fast and very very Reliable!