103040! - 1
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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:103040! - 1
Verification status (*):Proven
Official Comment:Factorial
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p301 : Winskill1, Fpsieve, PrimeGrid, OpenPFGW
Decimal Digits:471794   (log10 is 471793.32496352)
Rank (*):1294 (digit rank is 1)
Entrance Rank (*):136
Currently on list? (*):short
Submitted:12/14/2010 21:31:36 CDT
Last modified:12/18/2010 17:20:21 CDT
Database id:96944
Status Flags:none
Score (*):44.3267 (normalized score 2.3861)

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 4
Subcategory: "Factorial"
(archival tag id 213027, 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 (11 Sep 2014): 
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_id96944
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 1 103040 ! -1 2>&1
[Elapsed time: 40571.083 seconds]
modified2011-12-27 16:48:35
created2010-12-14 21:35:02
id123278

fieldvalue
prime_id96944
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -tp -q"103040!-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 103040!-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 103043, base 1+sqrt(103043)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(196608,19) to FFT(196608,18)
Reduced from FFT(196608,18) to FFT(196608,17)
Reduced from FFT(196608,17) to FFT(196608,16)
3134544 bit request FFT size=(196608,16)
Running N+1 test using discriminant 103043, base 2+sqrt(103043)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(196608,19) to FFT(196608,18)
Reduced from FFT(196608,18) to FFT(196608,17)
Reduced from FFT(196608,17) to FFT(196608,16)
3134544 bit request FFT size=(196608,16)
Calling Brillhart-Lehmer-Selfridge with factored part 33.98%
103040!-1 is prime! (328910.6907s+2.6303s)
[Elapsed time: 3.81 days]
modified2011-01-18 10:15:30
created2010-12-14 21:38:02
id123279

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