(436610099 - 1)/4365
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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

field (help)value
Description:(436610099 - 1)/4365
Verification status (*):PRP
Official Comment:Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x14 : Steward, Primo, OpenPFGW
Decimal Digits:36758   (log10 is 36757.565618889)
Rank (*):55717 (digit rank is 1)
Entrance Rank (*):35526
Currently on list? (*):short
Submitted:3/20/2011 08:24:09 CDT
Last modified:3/22/2011 18:15:57 CDT
Database id:99245
Status Flags:Verify
Score (*):36.4672 (normalized score 0.0007)

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 18
Subcategory: "Generalized Repunit"
(archival tag id 213172, tag last modified 2017-06-04 14:20:22)

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.

Andrew A. D. Steward writes (11 Sep 2014): 
Certificate at http://www.primes.viner-steward.org/andy/D/110E2773.html

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.
fieldvalue
prime_id99245
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"(4366^10099-1)/4365" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
(4366^10099-1)/4365 1/1 mro=0


trial factoring to 11674452
(4366^10099-1)/4365 has no small factor.
[Elapsed time: 34.821 seconds]
modified2011-12-27 16:48:33
created2011-03-20 08:35:16
id127881

fieldvalue
prime_id99245
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"(4366^10099-1)/4365" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing (4366^10099-1)/4365 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling N-1 BLS with factored part 0.45% and helper 0.00% (1.35% proof)
(4366^10099-1)/4365 is Fermat and Lucas PRP! (608.4494s+0.0015s)
[Elapsed time: 10.13 minutes]
modified2011-03-25 10:27:28
created2011-03-20 08:26:05
id127878

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.