113 · 2916801 + 1
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help

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:113 · 2916801 + 1
Verification status (*):Proven
Official Comment:Divides GF(916800,5), GF(916800,12)
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L153 : Eckhard, LLR
Decimal Digits:275987   (log10 is 275986.65413318)
Rank (*):15891 (digit rank is 1)
Entrance Rank (*):342
Currently on list? (*):short
Submitted:5/12/2009 05:09:03 CDT
Last modified:5/12/2009 19:48:56 CDT
Database id:88217
Status Flags:none
Score (*):42.6788 (normalized score 0.2935)

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 Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 18, weight 47.406233873725
Subcategory: "Divides GF(*,5)"
(archival tag id 210445, tag last modified 2016-03-15 13:57:15)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 16, weight 47.406233873725
Subcategory: "Divides GF(*,12)"
(archival tag id 210446, tag last modified 2016-03-15 13:57:15)

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.

Ruediger K. Eckhard writes (11 Sep 2014): 
A factor of xGF(916798,12,5).

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 113 2 916801 1 2>&1
[Elapsed time: 9.984 seconds]
modified2011-12-27 16:48:44
created2009-05-12 05:18:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"113*2^916801+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 113*2^916801+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(114688,20) to FFT(114688,19)
Reduced from FFT(114688,19) to FFT(114688,18)
Reduced from FFT(114688,18) to FFT(114688,17)
Reduced from FFT(114688,17) to FFT(114688,16)
1833624 bit request FFT size=(114688,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
113*2^916801+1 is prime! (4634.1654s+0.0008s)
[Elapsed time: 77.23 minutes]
modified2009-05-25 07:25:55
created2009-05-12 05:23:02

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