
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:  (4529^{16381}  1)/4528 
Verification status (*):  PRP 
Official Comment:  Generalized repunit 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  CH2 : Wu_T, Primo, OpenPFGW, CHG 
Decimal Digits:  59886 (log_{10} is 59885.318108689) 
Rank (*):  47996 (digit rank is 1) 
Entrance Rank (*):  37433 
Currently on list? (*):  short 
Submitted:  12/1/2012 18:52:57 CDT 
Last modified:  12/1/2012 19:50:25 CDT 
Database id:  110198 
Status Flags:  Verify 
Score (*):  37.9736 (normalized score 0.0031) 

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 6
Subcategory: "Generalized Repunit"
(archival tag id 214688, tag last modified 20170604 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.
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.
field  value 
prime_id  110198 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"(4529^163811)/4528" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (4529^163811)/4528 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 2 Running N1 test using base 23 Running N+1 test using discriminant 47, base 3+sqrt(47) Calling N1 BLS with factored part 0.55% and helper 0.00% (1.65% proof) (4529^163811)/4528 is Fermat and Lucas PRP! (1762.7384s+0.0032s) [Elapsed time: 29.38 minutes]

modified  20121219 19:14:49 
created  20121201 18:53:01 
id  150381 

field  value 
prime_id  110198 
person_id  9 
machine  Ditto P4 P4 
what  trial_divided 
notes  Command: /home/ditto/client/pfgw o f q"(4529^163811)/4528" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (4529^163811)/4528 1/1 mro=0
trial factoring to 19699746 (4529^163811)/4528 has no small factor. [Elapsed time: 93.624 seconds]

modified  20121219 19:14:49 
created  20121201 19:05:01 
id  150382 

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
