110059! + 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:110059! + 1
Verification status (*):Proven
Official Comment:Factorial
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p312 : Doggart, Fpsieve, PrimeGrid, OpenPFGW
Decimal Digits:507082   (log10 is 507081.17130001)
Rank (*):959 (digit rank is 1)
Entrance Rank (*):130
Currently on list? (*):short
Submitted:6/11/2011 05:54:32 CDT
Last modified:6/13/2011 10:20:23 CDT
Database id:100445
Status Flags:none
Score (*):44.5483 (normalized score 3.1264)

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.
Factorial primes (archivable *)
Prime on list: yes, rank 3
Subcategory: "Factorial"
(archival tag id 213307, tag last modified 2013-09-04 05:50:30)

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.

PrimeGrid writes (15 Jun 2011): 
For more information, please see the Official Announcement.

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_id100445
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 1 110059 ! 1 2>&1
[Elapsed time: 43420.107 seconds]
modified2011-12-27 16:48:32
created2011-06-11 06:05:01
id130454

fieldvalue
prime_id100445
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"110059!+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 110059!+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 110063
Running N-1 test using base 110069
Running N-1 test using base 110083
Calling Brillhart-Lehmer-Selfridge with factored part 33.77%
110059!+1 is prime! (186691.0525s+1.3367s)
[Elapsed time: 2.16 days]
modified2011-12-27 16:48:32
created2011-06-11 06:08:01
id130455

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.