Phi(5, (3668 · 16001# - 1) · (378266 · 16001#/5 + 1)7)

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

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 : Broadhurst, Caldwell, OpenPFGW
Decimal Digits:221071   (log10 is 221070.87932347)
Rank (*):25443 (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 0.0726)

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 150
Subcategory: "Generalized Unique"
(archival tag id 224226, tag last modified 2020-08-04 13:50:04)

User comments about this prime (disclaimer):

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David Broadhurst writes (11 May 2021):  (report abuse)
CHG proof with 28.125% factorization.

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]
modified2020-07-07 17:30:39
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]
modified2020-07-07 17:30:39
created2008-10-03 12:01:40
id100652

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
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