(288398317 - 1)/28838
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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:(288398317 - 1)/28838
Verification status (*):PRP
Official Comment:Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH6 : Steward, Primo, OpenPFGW, CHG
Decimal Digits:37090   (log10 is 37089.195333575)
Rank (*):55103 (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 0.0007)

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 16
Subcategory: "Generalized Repunit"
(archival tag id 190732, tag last modified 2017-02-04 08:50:35)

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): 
The certificate is available at http://www.primes.viner-steward.org/primes/D/70A7207D.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_id79010
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"(28839^8317-1)/28838" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 11787563
(28839^8317-1)/28838 has no small factor.
[Elapsed time: 35.910 seconds]
modified2007-03-03 21:00:43
created2006-12-16 11:22:01
id87119

fieldvalue
prime_id79010
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"(28839^8317-1)/28838" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing (28839^8317-1)/28838 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 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 N-1 BLS with factored part 0.55% and helper 0.02% (1.66% proof)
(28839^8317-1)/28838 is Fermat and Lucas PRP! (692.8586s+0.0224s)
[Elapsed time: 693 seconds]
modified2007-03-03 21:00:43
created2006-12-16 11:23:01
id87120

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.