(25807 + 1)/3
(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:(25807 + 1)/3
Verification status (*):PRP
Official Comment:Cyclotomy, generalized Lucas number, Wagstaff
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):PM : Mihailescu
Decimal Digits:1748   (log10 is 1747.60406357)
Rank (*):94491 (digit rank is 4)
Entrance Rank (*):19478
Currently on list? (*):short
Submitted:1998
Last modified:11/29/2004 15:55:01 CDT
Database id:72546
Status Flags:Verify
Score (*):27.0163 (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.
Cyclotomy Proof (tolerated *)
Prime on list: no, rank 117
Subcategory: "Cyclotomy Proof"
(archival tag id 181341, tag last modified 2005-12-06 08:20:23)
Generalized Lucas Number (archivable *)
Prime on list: no, rank 96
Subcategory: "Generalized Lucas Number"
(archival tag id 181340, tag last modified 2016-05-02 05:50:25)
Wagstaff (archivable *)
Prime on list: yes, rank 8
Subcategory: "Wagstaff"
(archival tag id 181342, tag last modified 2014-09-17 12:50:33)

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.

Chris Caldwell writes (11 Sep 2014): 
notes

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_id72546
person_id9
machineLinux P4 2.8GHz
whatprp
notesCommand: /home/caldwell/client/pfgw -f -tc -q"(2^5807+1)/3" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing (2^5807+1)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 431245
Running N-1 test using base 2
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(768,22) to FFT(768,21)
Reduced from FFT(768,21) to FFT(768,20)
Reduced from FFT(768,20) to FFT(768,19)
Reduced from FFT(768,19) to FFT(768,18)
Reduced from FFT(768,18) to FFT(768,17)
Reduced from FFT(768,17) to FFT(768,16)
11620 bit request FFT size=(768,16)
Running N-1 test using base 5
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(768,22) to FFT(768,21)
Reduced from FFT(768,21) to FFT(768,20)
Reduced from FFT(768,20) to FFT(768,19)
Reduced from FFT(768,19) to FFT(768,18)
Reduced from FFT(768,18) to FFT(768,17)
Reduced from FFT(768,17) to FFT(768,16)
11620 bit request FFT size=(768,16)
Running N+1 test using discriminant 13, base 1+sqrt(13)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(768,22) to FFT(768,21)
Reduced from FFT(768,21) to FFT(768,20)
Reduced from FFT(768,20) to FFT(768,19)
Reduced from FFT(768,19) to FFT(768,18)
Reduced from FFT(768,18) to FFT(768,17)
Reduced from FFT(768,17) to FFT(768,16)
11628 bit request FFT size=(768,16)
Running N+1 test using discriminant 13, base 2+sqrt(13)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(768,22) to FFT(768,21)
Reduced from FFT(768,21) to FFT(768,20)
Reduced from FFT(768,20) to FFT(768,19)
Reduced from FFT(768,19) to FFT(768,18)
Reduced from FFT(768,18) to FFT(768,17)
Reduced from FFT(768,17) to FFT(768,16)
11628 bit request FFT size=(768,16)
Calling N+1 BLS with factored part 1.71% and helper 0.79% (5.94% proof)
(2^5807+1)/3 is Fermat and Lucas PRP! (4.3552s+0.0003s)
modified2004-12-06 15:06:28
created2004-11-29 15:55:56
id77544

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