primU(67825)
(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:primU(67825)
Verification status (*):PRP
Official Comment:Fibonacci primitive part
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x23 : Renze, Water, Broadhurst, Primo, OpenPFGW
Decimal Digits:11336   (log10 is 11335.493123964)
Rank (*):72015 (digit rank is 1)
Entrance Rank (*):32358
Currently on list? (*):short
Submitted:2/15/2007 04:02:38 CDT
Last modified:2/15/2007 04:24:27 CDT
Database id:79401
Status Flags:Verify
Score (*):32.8285 (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.
Fibonacci Primitive Part (archivable *)
Prime on list: yes, rank 3
Subcategory: "Fibonacci Primitive Part"
(archival tag id 194080, tag last modified 2015-04-16 11:20:32)

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.

David Broadhurst writes (11 Sep 2014): 
CHG proof at 26.84% in http://physics.open.ac.uk/~dbroadhu/cert/fs67825.zip

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_id79401
person_id9
machineRedHat P4 P4
whattrial_divided
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
3112604665...5453201662.........4228166381065827 1/1


trial factoring to 3290116
3112604665...7356204001 has no small factor.
[Elapsed time: 18.358 seconds]
modified2007-03-03 21:00:42
created2007-02-15 04:22:01
id87903

fieldvalue
prime_id79401
person_id9
machineRedHat P4 P4
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 3112604665...7356204001 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(5120,21) to FFT(5120,20)
Reduced from FFT(5120,20) to FFT(5120,19)
Reduced from FFT(5120,19) to FFT(5120,18)
Reduced from FFT(5120,18) to FFT(5120,17)
Reduced from FFT(5120,17) to FFT(5120,16)
75320 bit request FFT size=(5120,16)
Running N-1 test using base 17
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(5120,21) to FFT(5120,20)
Reduced from FFT(5120,20) to FFT(5120,19)
Reduced from FFT(5120,19) to FFT(5120,18)
Reduced from FFT(5120,18) to FFT(5120,17)
Reduced from FFT(5120,17) to FFT(5120,16)
75320 bit request FFT size=(5120,16)
Running N+1 test using discriminant 29, base 4+sqrt(29)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(5120,21) to FFT(5120,20)
Reduced from FFT(5120,20) to FFT(5120,19)
Reduced from FFT(5120,19) to FFT(5120,18)
Reduced from FFT(5120,18) to FFT(5120,17)
Reduced from FFT(5120,17) to FFT(5120,16)
75328 bit request FFT size=(5120,16)
Calling N-1 BLS with factored part 1.45% and helper 0.00% (4.35% proof)
3112604665...7356204001 is Fermat and Lucas PRP! (84.3000s+0.0100s)
[Elapsed time: 86 seconds]
modified2007-02-15 04:24:27
created2007-02-15 04:23:01
id87905

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