
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:  (34120^{11311}  1)/34119 
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:  51269 (log_{10} is 51268.332057152) 
Rank (*):  51606 (digit rank is 2) 
Entrance Rank (*):  32834 
Currently on list? (*):  short 
Submitted:  9/1/2011 14:53:48 CDT 
Last modified:  9/1/2011 15:50:25 CDT 
Database id:  101439 
Status Flags:  Verify 
Score (*):  37.4943 (normalized score 0.0018) 

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 11
Subcategory: "Generalized Repunit"
(archival tag id 213407, tag last modified 20180124 23:20:10)
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  101439 
person_id  9 
machine  Ditto P4 P4 
what  trial_divided 
notes  Command: /home/ditto/client/pfgw o f q"(34120^113111)/34119" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] (34120^113111)/34119 1/1 mro=0
trial factoring to 16679901 (34120^113111)/34119 has no small factor. [Elapsed time: 68.275 seconds]

modified  20111227 16:48:29 
created  20110901 15:05:05 
id  132443 

field  value 
prime_id  101439 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"(34120^113111)/34119" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing (34120^113111)/34119 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 13 Running N+1 test using discriminant 37, base 15+sqrt(37) Calling N1 BLS with factored part 0.36% and helper 0.01% (1.08% proof) (34120^113111)/34119 is Fermat and Lucas PRP! (1436.7923s+0.0283s) [Elapsed time: 23.95 minutes]

modified  20111227 16:48:29 
created  20110901 15:23:01 
id  132445 

Query times: 0.0006 seconds to select prime, 0.0007 seconds to seek comments.
