(3412011311 - 1)/34119
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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:(3412011311 - 1)/34119
Verification status (*):PRP
Official Comment:Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH2 : Wu_T, CHG, Primo, OpenPFGW
Decimal Digits:51269   (log10 is 51268.332057152)
Rank (*):45955 (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 0.0026)

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 5
Subcategory: "Generalized Repunit"
(archival tag id 213407, tag last modified 2013-05-11 04:20:32)

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.

Tom Wu writes (1 Sep 2011): 
CHG proof at 29.6% available at:
http://xenon.stanford.edu/~tjw/pp/34120_11311/index.html
This proof relies on an ECPP certificate of a 12155-digit helper prime that divides N-1.

At time of posting, this prime set records for both the largest GRU (generalized repunit) prime and the largest NTG (non-trivial gigantic) prime. For more details, see the primenumbers discussion thread.

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_id101439
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"(34120^11311-1)/34119" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
(34120^11311-1)/34119 1/1 mro=0


trial factoring to 16679901
(34120^11311-1)/34119 has no small factor.
[Elapsed time: 68.275 seconds]
modified2011-12-27 16:48:29
created2011-09-01 15:05:05
id132443

fieldvalue
prime_id101439
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"(34120^11311-1)/34119" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing (34120^11311-1)/34119 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N+1 test using discriminant 37, base 15+sqrt(37)
Calling N-1 BLS with factored part 0.36% and helper 0.01% (1.08% proof)
(34120^11311-1)/34119 is Fermat and Lucas PRP! (1436.7923s+0.0283s)
[Elapsed time: 23.95 minutes]
modified2011-12-27 16:48:29
created2011-09-01 15:23:01
id132445

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