
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:  (28839^{8317}  1)/28838 
Verification status (*):  PRP 
Official Comment:  Generalized repunit 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  CH6 : Steward, Primo, OpenPFGW, CHG 
Decimal Digits:  37090 (log_{10} is 37089.195333575) 
Rank (*):  57186 (digit rank is 1) 
Entrance Rank (*):  16151 
Currently on list? (*):  short 
Submitted:  12/16/2006 10:55:39 CDT 
Last modified:  12/16/2006 11:34:34 CDT 
Database id:  79010 
Status Flags:  Verify 
Score (*):  36.495 (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 19
Subcategory: "Generalized Repunit"
(archival tag id 190732, 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  79010 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f q"(28839^83171)/28838" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 11787563 (28839^83171)/28838 has no small factor. [Elapsed time: 35.910 seconds]

modified  20070303 21:00:43 
created  20061216 11:22:01 
id  87119 

field  value 
prime_id  79010 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"(28839^83171)/28838" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (28839^83171)/28838 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) 246424 bit request FFT size=(14336,18) Running N+1 test using discriminant 41, base 18+sqrt(41) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(14336,20) to FFT(14336,19) Reduced from FFT(14336,19) to FFT(14336,18) 246432 bit request FFT size=(14336,18) Calling N1 BLS with factored part 0.55% and helper 0.02% (1.66% proof) (28839^83171)/28838 is Fermat and Lucas PRP! (692.8586s+0.0224s) [Elapsed time: 693 seconds]

modified  20070303 21:00:43 
created  20061216 11:23:01 
id  87120 

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
