Phi(5, (3668 · 16001# - 1) · (378266 · 16001#/5 + 1)7)
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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:Phi(5, (3668 · 16001# - 1) · (378266 · 16001#/5 + 1)7)
Verification status (*):PRP
Official Comment:Generalized unique
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):x34 : Caldwell, Broadhurst, OpenPFGW
Decimal Digits:221071   (log10 is 221070.87932347)
Rank (*):19539 (digit rank is 1)
Entrance Rank (*):505
Currently on list? (*):no
Submitted:10/1/2008 09:45:28 CDT
Last modified:10/3/2008 12:13:53 CDT
Database id:85584
Status Flags:Verify
Score (*):41.9964 (normalized score 0.1719)

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.
Generalized Unique (archivable *)
Prime on list: no, rank 144
Subcategory: "Generalized Unique"
(archival tag id 209002, tag last modified 2017-11-01 02:50:22)

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): 
Data for the CHG proof, with 28.125% factorization, is here, giving the output here. The BLS tests are here.

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_id85584
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"Phi(5,(3668*16001#-1)*(378266*16001#/5+1)^7)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
trial factoring to 79437167
Phi(5,(3668*16001#-1)*(378266*16001#/5+1)^7) has no small factor.
[Elapsed time: 1289.182 seconds]
modified2011-12-27 16:48:46
created2008-10-01 09:52:01
id100637

fieldvalue
prime_id85584
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -hhelper -q"Phi(5,(3668*16001#-1)*(378266*16001#/5+1)^7)" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing Phi(5,(3668*16001#-1)*(378266*16001#/5+1)^7) [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper
Running N-1 test using base 16033
Running N-1 test using base 16061
Running N-1 test using base 16063
Running N-1 test using base 16067
Running N+1 test using discriminant 16103, base 6+sqrt(16103)
Calling N-1 BLS with factored part 28.13% and helper 0.00% (84.38% proof)
Phi(5,(3668*16001#-1)*(378266*16001#/5+1)^7) is Fermat and Lucas PRP! (95089.6385s+0.4037s)
[Elapsed time: 26.41 hours]
modified2008-11-16 12:15:22
created2008-10-03 12:01:40
id100652

Query times: 0.0016 seconds to select prime, 0.0003 seconds to seek comments.