(362109319 - 1)/36209

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Description:(362109319 - 1)/36209
Verification status (*):PRP
Official Comment (*):Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p170 : Wu_T, Primo, OpenPFGW
Decimal Digits:42480   (log10 is 42479.164206239)
Rank (*):58565 (digit rank is 1)
Entrance Rank (*):55393
Currently on list? (*):short
Submitted:3/31/2019 02:32:54 CDT
Last modified:3/31/2019 02:50:24 CDT
Database id:126349
Status Flags:Verify, TrialDiv
Score (*):36.9139 (normalized score 0.0005)

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 Repunit (archivable *)
Prime on list: yes, rank 20
Subcategory: "Generalized Repunit"
(archival tag id 220195, tag last modified 2020-11-08 16:50:07)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Tom Wu writes (31 Mar 2019):  (report abuse)
BLS primality proof (N-1)

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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"(36210^9319-1)/36209" 2>&1 PFGW Version [GWNUM 27.11] Primality testing (36210^9319-1)/36209 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N-1 test using base 13 Running N+1 test using discriminant 23, base 1+sqrt(23) Calling N-1 BLS with factored part 0.07% and helper 0.02% (0.24% proof) (36210^9319-1)/36209 is Fermat and Lucas PRP! (225.4790s+0.0010s) [Elapsed time: 3.77 minutes]
modified2020-07-07 17:30:13
created2019-03-31 02:33:01

Query times: 0.0005 seconds to select prime, 0.0009 seconds to seek comments.
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