20210421, 15:04  #12 
Jun 2003
3^{4}×67 Posts 
Serge, one question. Does LLR use standard PRP test, 3^(N1) == 1, or does it do 3^10^p == 3^10?

20210421, 15:25  #13 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
23406_{8} Posts 
We finished 3PRP, 7PRP, 11PRP, 13PRP (and their SPRP chasers are still running, the Lucas+Frobenius test phases  they are ~10x slower even on 32 threads).

20210421, 15:28  #14 
Sep 2002
Database er0rr
29×151 Posts 

20210421, 15:33  #15  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9990_{10} Posts 
Quote:
For N not being near a power of 2, there is no expected savings of doing exponentiation to N1, to N or to N+1 (for Mersennes, for example). N1 is just a binary string of both "1"s and "0"s, no difference from N or even 9N. 

20210421, 16:01  #16 
Jun 2003
3^{4}×67 Posts 
But 9N+1 = 10^p = 5^p*2^p has a lot more zeros than 1s. Honestly, I don't know what is the impact of simple squaring vs squaring*3. Once upon a time, I recall there being low single digit % difference in performance between LLR and PRP on Riesel numbers (all 1s), but I could be mistaken.

20210421, 16:07  #17 
Jan 2007
Germany
572_{10} Posts 
Congratulation , this is so cool !

20210421, 16:18  #18  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·3^{3}·5·37 Posts 
Quote:
Worth trying; interesting. llr is not doing it now, but we can hack a patch, and test the speed gain (if it exists). 

20210421, 16:36  #19 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2·47·109 Posts 

20210421, 17:19  #20  
Jun 2003
3^{4}×67 Posts 
Quote:
PS: In theory, even the 3^5^p could be protected by GEC, but it will cost 50% extra  worth it only if used as an alternative for double checks 

20210421, 20:05  #21  
"Robert Gerbicz"
Oct 2005
Hungary
7·229 Posts 
Quote:
a^(b^n)=a^(B^(n/e)) and you can do the error checking using this new base, if we count only the squarings then the extra cost of using B>2 is ceil(log2(B))/log2(B)1 in 1 part. [for B=2 this is zero]. One small drawback here is that when you would want to choose very large e so large B to lower the overhead then you can't error check that very frequently. 

20210421, 20:51  #22  
Mar 2011
Germany
97_{10} Posts 
Quote:
Congratulations on finding the next repunit prime, well done. I can give some infos on the current repunit search that our team is doing: I extended the original database from skoberne (with complete new structure), but it is not publicly available. So every few weeks I send a new excerpt to Kurt, so his website Kurt's subpage is officially the new live site, but so far only up to n=6000000. The database itself contains all prime exponents up to 10000000, including known factors, Res64 and/or Res2048 values plus the current bitdepth of sieving. If somebody is interested I can send him a complete dump, or extract the needed information, just send me a PM. As of today we have tested all of the exponents up to 4880957, with the exception of very few numbers around 4300459 (still waiting for the results of one user). So how was the new number found, by random selection or systematic search? If you are still in favor of a systematic search we could combine our efforts. Currently I am doing a manual reservation of exponents via email, nothing like the professional search for Mersenne primes. I would also suggest that you try out running the PRP test with prime95/mprime, it should be faster than llr. E.g. running the test for the found prp has the worktodo entry PRP=1,10,5794777,1,99,0,3,1,"9" I am currently running the test with mprime on an 8 Core AMD, will post the results here once finished. Cheers, Danilo PS.: @Batalov, I didn't see your comment on LLR vs mprime, only later. I should compare again, last time I tested mprime was like 10% faster. Also I am using it to get the Res2048 value, does LLR has the similar option to get the long residue? Last fiddled with by MrRepunit on 20210421 at 21:13 Reason: llr vs mprime was already discussed 

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