
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:  (40734^{16111}  1)/40733 
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:  74267 (log_{10} is 74266.408232087) 
Rank (*):  47675 (digit rank is 1) 
Entrance Rank (*):  40903 
Currently on list? (*):  short 
Submitted:  3/9/2015 00:59:43 CDT 
Last modified:  3/9/2015 01:20:31 CDT 
Database id:  119521 
Status Flags:  Verify, TrialDiv 
Score (*):  38.6373 (normalized score 0.0039) 

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 2
Subcategory: "Generalized Repunit"
(archival tag id 217915, tag last modified 20180909 08:20:06)
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  119521 
person_id  9 
machine  Using: Xeon 4c+4c 3.5GHz 
what  prp 
notes  Command: /home/caldwell/client/pfgw/pfgw64 tc q"(40734^161111)/40733" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing (40734^161111)/40733 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 2 Running N1 test using base 3 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N1 BLS with factored part 0.14% and helper 0.00% (0.42% proof)
(40734^161111)/40733 is Fermat and Lucas PRP! (600.1030s+0.0017s) [Elapsed time: 10.00 minutes]

modified  20150420 07:32:09 
created  20150309 01:01:01 
id  165129 

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.
