(V(77786, 1, 6453) + 1)/(V(77786, 1, 27) + 1)

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Description:(V(77786, 1, 6453) + 1)/(V(77786, 1, 27) + 1)
Verification status (*):PRP
Official Comment (*):Lehmer primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x25 : Broadhurst, Water, OpenPFGW, Primo
Decimal Digits:31429   (log10 is 31428.932648348)
Rank (*):62973 (digit rank is 1)
Entrance Rank (*):47767
Currently on list? (*):short
Submitted:12/26/2012 11:13:59 CDT
Last modified:12/26/2012 11:50:25 CDT
Database id:110481
Status Flags:Verify
Score (*):35.9835 (normalized score 0.0002)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.
Lehmer primitive part (archivable *)
Prime on list: yes, rank 4
Subcategory: "Lehmer primitive part"
(archival tag id 214827, tag last modified 2019-08-26 13:20:28)

User comments about this prime (disclaimer):

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David Broadhurst writes (11 Sep 2014):  (report abuse)

CHG proof at 31429 digits and 26.19% factorization with details in http://physics.open.ac.uk/~dbroadhu/cert/lh77786.zip and a certificate compressed to 25MB in http://physics.open.ac.uk/~dbroadhu/cert/lh77786_cert.gp.gz

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f -q"(lucasV(77786,1,6453)+1)/(lucasV(77786,1,27)+1)" 2>&1 PFGW Version [GWNUM 26.5] (lucasV(77786,1,....V(77786,1,27)+1) 1/1 mro=0 trial factoring to 9867605 (lucasV(77786,1,6453)+1)/(lucasV(77786,1,27)+1) has no small factor. [Elapsed time: 25.563 seconds]
modified2020-07-07 17:30:23
created2012-12-26 11:18:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tc -q"(lucasV(77786,1,6453)+1)/(lucasV(77786,1,27)+1)" 2>&1 PFGW Version [GWNUM 26.5] Primality testing (lucasV(77786,1,6453)+1)/(lucasV(77786,1,27)+1) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 59 Running N-1 test using base 109 Running N-1 test using base 113 Running N-1 test using base 151 Running N+1 test using discriminant 163, base 24+sqrt(163) Calling N-1 BLS with factored part 1.58% and helper 0.06% (4.80% proof) (lucasV(77786,1,6453)+1)/(lucasV(77786,1,27)+1) is Fermat and Lucas PRP! (819.2734s+0.0062s) [Elapsed time: 13.65 minutes]
modified2020-07-07 17:30:23
created2012-12-26 11:23:01

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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