primV(111534, 1, 27000)

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Description:primV(111534, 1, 27000)
Verification status (*):PRP
Official Comment (*):Generalized Lucas primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x25 : Broadhurst, Water, OpenPFGW, Primo
Decimal Digits:72683   (log10 is 72682.664799838)
Rank (*):49821 (digit rank is 1)
Entrance Rank (*):38122
Currently on list? (*):short
Submitted:11/15/2013 07:01:15 CDT
Last modified:11/15/2013 08:21:21 CDT
Database id:116319
Status Flags:Verify, TrialDiv
Score (*):38.5708 (normalized score 0.0028)

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.
Generalized Lucas primitive part (archivable *)
Prime on list: yes, rank 1
Subcategory: "Generalized Lucas primitive part"
(archival tag id 217445, tag last modified 2013-11-15 08:21:24)

User comments about this prime (disclaimer):

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David Broadhurst writes (11 Sep 2014):  (report abuse)
CHG proof at 72683 digits and 26.29% factorization, with details in and a certificate compressed to 43 MB in It is notable that no use of ECPP was required for this proof, since the 9692-digit helper primV(111534,1,3600) was proven by BLS. All other helpers had less than 600 digits and were proven by Pari-GP. At time of posting, primV(111534,1,27000) occupied first place at

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"primV(111534,1,27000)" 2>&1 PFGW Version [GWNUM 26.5] Primality testing primV(111534,1,27000) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N-1 test using base 41 Running N+1 test using discriminant 59, base 4+sqrt(59) Calling N-1 BLS with factored part 0.81% and helper 0.01% (2.43% proof) primV(111534,1,27000) is Fermat and Lucas PRP! (2843.2577s+0.3164s) [Elapsed time: 47.38 minutes]
modified2020-07-07 17:30:18
created2013-11-15 07:08:02

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