2072644824759 · 233333 + 5
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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:2072644824759 · 233333 + 5
Verification status (*):PRP
Official Comment:Triplet (3), ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):FE5 : Luhn, Morain, FastECPP
Decimal Digits:10047   (log10 is 10046.549370354)
Rank (*):72714 (digit rank is 2)
Entrance Rank (*):39226
Currently on list? (*):short
Submitted:11/18/2008 07:06:55 CDT
Last modified:11/20/2008 19:20:03 CDT
Database id:85776
Status Flags:Verify
Score (*):32.4545 (normalized score 0)

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.
Triplet (archivable class *)
Prime on list: yes, rank 5
Subcategory: "Triplet (3)"
(archival tag id 194284, tag last modified 2015-08-31 10:50:38)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 154
Subcategory: "ECPP"
(archival tag id 194283, tag last modified 2017-09-09 11:20:24)

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.

Norman Luhn writes (11 Sep 2014): 
The certificate you find here: http://www.lix.polytechnique.fr/Labo/Francois.Morain/Primes/Certif/luhn.certif.gz

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_id85776
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 2072644824759 2 33333 5 2>&1
[Elapsed time: 8.213 seconds]
modified2011-12-27 16:48:46
created2008-11-18 07:22:18
id101024

fieldvalue
prime_id85776
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"2072644824759*2^33333+5" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2072644824759*2^33333+5 [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(4096,21) to FFT(4096,20)
Reduced from FFT(4096,20) to FFT(4096,19)
Reduced from FFT(4096,19) to FFT(4096,18)
Reduced from FFT(4096,18) to FFT(4096,17)
66756 bit request FFT size=(4096,17)
Running N+1 test using discriminant 5, base 4+sqrt(5)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(4096,21) to FFT(4096,20)
Reduced from FFT(4096,20) to FFT(4096,19)
Reduced from FFT(4096,19) to FFT(4096,18)
Reduced from FFT(4096,18) to FFT(4096,17)
66764 bit request FFT size=(4096,17)
Running N+1 test using discriminant 5, base 5+sqrt(5)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(4096,21) to FFT(4096,20)
Reduced from FFT(4096,20) to FFT(4096,19)
Reduced from FFT(4096,19) to FFT(4096,18)
Reduced from FFT(4096,18) to FFT(4096,17)
66764 bit request FFT size=(4096,17)
Calling N+1 BLS with factored part 0.10% and helper 0.06% (0.38% proof)
2072644824759*2^33333+5 is Fermat and Lucas PRP! (66.5500s+0.0000s)
[Elapsed time: 67.00 seconds]
modified2009-02-05 12:51:36
created2008-11-18 07:08:15
id101021

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.