R(1031)
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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:R(1031)
Verification status (*):Proven
Official Comment:Repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):WD : Dubner, Williams, Cruncher
Decimal Digits:1031   (log10 is 1030.04575749056)
Rank (*):113022 (digit rank is 57)
Entrance Rank (*):565
Currently on list? (*):short
Submitted:1985
Last modified:1985
Database id:55968
Status Flags:none
Score (*):25.3646 (normalized score 0)

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.
Repunit (archivable *)
Prime on list: yes, rank 1
Subcategory: "Repunit"
(archival tag id 186344, tag last modified 2008-10-02 15:50:05)

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.

David Broadhurst writes (11 Sep 2014): 
An "external" proof may be found here.

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_id55968
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tc -hhelp1031 -q"R(1031)" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing R(1031) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file help1031
Running N-1 test using base 7
Running N+1 test using discriminant 29, base 2+sqrt(29)
Calling N-1 BLS with factored part 40.49% and helper 0.09% (121.60% proof)
R(1031) is prime! (0.4723s+0.0003s)
[Elapsed time: 0.00 seconds]
Helper File:
7034077
Phi(103,10)/1031/7034077
44092859
102860539
984385009
612053256358933
182725114866521155647161
Phi(206,10)/1237/44092859/102860539/984385009/612053256358933/182725114866521155647161
5905014721
326345481191
2702394989404991
7073532436575439739956079653594194521
85517237338860102283865323577960208481
497491
569836171
2013681931
567664121498896654896380203841
896048585318577702680084550566846611
modified2011-04-15 10:07:17
created2011-03-30 21:56:24
id128098

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