(113797411 - 1)/11378
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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:(113797411 - 1)/11378
Verification status (*):PRP
Official Comment:Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x14 : Steward, Primo, OpenPFGW
Decimal Digits:30056   (log10 is 30055.731400068)
Rank (*):58717 (digit rank is 1)
Entrance Rank (*):30690
Currently on list? (*):short
Submitted:12/31/2009 05:10:05 CDT
Last modified:3/22/2011 18:18:41 CDT
Database id:91331
Status Flags:Verify
Score (*):35.8454 (normalized score 0.0003)

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 20
Subcategory: "Generalized Repunit"
(archival tag id 210592, tag last modified 2017-06-04 14:20:22)

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): 
Certificate at http://www.primes.viner-steward.org/andy/E/2C731CF3.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_id91331
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"(11379^7411-1)/11378" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 9405208
(11379^7411-1)/11378 has no small factor.
[Elapsed time: 23.400 seconds]
modified2011-12-27 16:48:41
created2009-12-31 05:18:02
id112037

fieldvalue
prime_id91331
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"(11379^7411-1)/11378" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing (11379^7411-1)/11378 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(12288,21) to FFT(12288,20)
Reduced from FFT(12288,20) to FFT(12288,19)
Reduced from FFT(12288,19) to FFT(12288,18)
Reduced from FFT(12288,18) to FFT(12288,17)
199694 bit request FFT size=(12288,17)
Running N-1 test using base 19
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(12288,21) to FFT(12288,20)
Reduced from FFT(12288,20) to FFT(12288,19)
Reduced from FFT(12288,19) to FFT(12288,18)
Reduced from FFT(12288,18) to FFT(12288,17)
199694 bit request FFT size=(12288,17)
Running N+1 test using discriminant 37, base 15+sqrt(37)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(12288,21) to FFT(12288,20)
Reduced from FFT(12288,20) to FFT(12288,19)
Reduced from FFT(12288,19) to FFT(12288,18)
Reduced from FFT(12288,18) to FFT(12288,17)
199702 bit request FFT size=(12288,17)
Calling N-1 BLS with factored part 0.54% and helper 0.00% (1.61% proof)
(11379^7411-1)/11378 is Fermat and Lucas PRP! (514.2700s+0.0000s)
[Elapsed time: 8.68 minutes]
modified2010-03-13 18:56:31
created2009-12-31 05:12:38
id112036

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.