20111106, 18:52  #1 
"William"
May 2003
New Haven
2^{2}·3^{2}·5·13 Posts 
Share N+/1 Primality Proofs
This thread is for sharing N+/1 primality proofs completed in the factordb. It's purpose is to share the fun and encourage others to take up the hobby.
Today I spotted (305^6171)/304 in the PRP list. N1 is (305^6161)/304, which has many algebraic factors although the factordb doesn't find them. I added enough of these to N1 to complete the primality proof. It used to be easy to spot situations like this, but between the recent increase in the minimum level of PRPs and careful scanning of a few people, they are getting harder to find. 
20111107, 02:16  #2  
Romulan Interpreter
Jun 2011
Thailand
21254_{8} Posts 
Quote:


20111108, 15:21  #3 
"William"
May 2003
New Haven
2^{2}×3^{2}×5×13 Posts 
Today a spotted (721^4571)/720, which needed the algebraic factors of 721^4561 to complete the N1 proof.

20111108, 15:31  #4  
Nov 2003
2^{6}·113 Posts 
Quote:
numbers that are easily dealt with by more modern methods??? It is pointless. 

20111108, 19:35  #5  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10131_{10} Posts 
Quote:
Quite often I optimize human time over CPU time. Paul 

20111108, 19:45  #6  
Nov 2003
2^{6}×113 Posts 
Quote:
greater mathematical knowledge if one is writing the source code. Note also that APRCL can/does take advantage of known factors of N+1 and/or N1 to speed the computation. 

20111108, 20:14  #7 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}×7×163 Posts 
CHG is also fun to use at about 26 to 27% N+/1 factored... just like solving a sudoku at a coffee break. (above 27%, it is simply not fun anymore :) )
Example: 110Β·R53821 is prime. Proven with CHG. (not in FactorDB.) Last fiddled with by Batalov on 20111108 at 20:19 Reason: Example 
20111108, 20:19  #8  
"William"
May 2003
New Haven
4444_{8} Posts 
Quote:
Everybody dealing with archiving primality proofs picks a threshold of "below here is trivial and left as exercise for the reader, above here I archive the proof. For his site about Titanic Prime Generalized Repunits, Andy Steward uses 250 digits  all helper primes above that length have proofs on his web site, but below that there is only the assertion that they have been proven. The factordb uses a 300 digit cutoff. Below this the factordb detects PRPs, marks them as PRP in the database, then schedules a proof. Upon passing the proof, the status is changed from PRP to P. Above this level the factordb support N+/1 proofs and ECPP certificates. The helper files and certificates can be downloaded by anybody wanting to verify the proof. There is a database report that shows the PRPs, and an interface to download these. There are people who download these, generate Primo proofs, and upload the certificates. I generate these proofs in part because it is even more pointless to generate an ECPP proof for a number with easily detected N+1 and N1 factors. In addition, I get a kick out of seeing the status change from PRP to P. Yes pointless  but most of I what I do at MersenneForum is pointless. I don't let that stop me. 

20111108, 22:41  #9  
Nov 2003
2^{6}·113 Posts 
Quote:
would use obsolete methods when newer/better methods are readily available and are no harder to use. 

20111109, 02:43  #10  
"William"
May 2003
New Haven
2^{2}·3^{2}·5·13 Posts 
Quote:
Observation: There is an elegance about using factorization based proofs in a system that is dedicated to storing factorizations. Much of the infrastructure needed to create the proofs is already designed into the core of the system. Question: What primality proving method do you recommend for (721^4571)/720? 

20111109, 04:24  #11 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}·7·163 Posts 
Questionvariant 2: What primality proving method do you recommend for (721^4611)/720 (the next PRP in the same (721^n1)/720 series)?
CHG would work, but Primo is also fast for this size. For Syd: there's a CHG verifying script by D.Broadhurst; so CHG certificates could also be accepted for download. 
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