20210204, 15:15  #45  
Jun 2009
700_{10} Posts 
Quote:
The way Primo works is (very simply put) as follows: it looks for a number that is slightly smaller than the candidate (how much smaller is given as "gain" in bits) in such a way that the candidate is prime if the slightly smaller numer is prime. Then it repeats this process with smaller and smaller numbers until it reaches a very small number that is known to be prime. Sometimes Primo cannot find such a smaller number. In such cases it backtracks, trying to find another helper number for the last step or the step before etc. I think backtracking is limited to 10 steps. If there are only dead ends, Primo is unably to prove the candidate prime. This happens usually at the beginning of a run when there is no or very little chance of backtracking. I don't know about the latest versions, but a few years ago, the largest number that Primo was guaranteed to be able to prove was less than a third (in terms of digits) of the largest numbers it was able to prove. So there is always a chance of failure and it's getting bigger with larger candidates. Try contacting Marcel anyway as there might be another cause. 

20210204, 19:48  #46 
Sep 2002
Database er0rr
2^{3}×3×11×17 Posts 
@Gelly
You might find that altering the settings under "Menu" will get you further, most likely a proof. I cant's recall what it is called, but I think it goes up to "32". You most likely would have to start from the beginning. Also I am getting great thoughput by running two numbers at once. There are plenty of free cycles during phase 1. You can see what is happening by running top in a console. (I am running nice n 5 on the main number and nice n 19 on the subsidiary one. I am using all threads, but there is a slight impact on turbo.) Last fiddled with by paulunderwood on 20210204 at 20:36 
20210204, 20:38  #47 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89×113 Posts 
I think there is also randomness in proof and/or user can induce the proof going different paths: change some options in settings. E.g. if you change the highlighted options, it will give up optimizing gain earlier or later, and you might pass the 1st test and then it will go forward.

20210224, 06:38  #48  
Sep 2002
Database er0rr
2^{3}×3×11×17 Posts 
Quote:
FactorDB entry Last fiddled with by paulunderwood on 20210224 at 06:38 

20210315, 16:58  #49 
Sep 2002
Database er0rr
2^{3}×3×11×17 Posts 
Reserving:
Code:
M86137 cofactor prp25896 M86371 cofactor prp25984 M87691 cofactor prp26371 E(11848)/(5*1582043) prp40792 
20210423, 15:07  #50 
May 2020
47_{10} Posts 
Done! 6693424s (77.5 days). I'll first be tinkering with the cofactor of Bern(8286) (hopefully a monthish at most), but after seeing Paul go hogwild on reservations, my next reservation is PRP32010, or M106391/286105171290931103.

20210428, 00:02  #51  
Sep 2002
Database er0rr
10610_{8} Posts 
Quote:
Those 4 I reserved are running on a relatively slow Xeon Phi which has 256 threads. An instance of Primo often drops to one thread, So, in the long term I should get some nice throughput. Last fiddled with by paulunderwood on 20210428 at 00:07 

20210504, 19:25  #52 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10011101001001_{2} Posts 
Asuncion & Allombert did the fib(130021) proof,
but it remains to be seen if it was some other ECPP or even a hybrid proof. They are folks widely known in narrow circles (Pari/GP team, INRIA). 
20210504, 19:41  #53  
Sep 2002
Database er0rr
2^{3}·3·11·17 Posts 
Quote:


20210505, 00:05  #54 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
89·113 Posts 

20210505, 02:09  #55  
Sep 2002
Database er0rr
1188_{16} Posts 
Bill Allombert replied to my enquiry to him about the certiifcation of U(130021):
Quote:


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