
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. 
Proofcode(s): (*):  x34 : Caldwell, Broadhurst, OpenPFGW 
Decimal Digits:  221071 (log_{10} is 221070.87932347) 
Rank (*):  19453 (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 0.1748) 

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 134
Subcategory: "Generalized Unique"
(archival tag id 209002, tag last modified 20170424 12:50:25)
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.
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.
field  value 
prime_id  85584 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /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]

modified  20111227 16:48:46 
created  20081001 09:52:01 
id  100637 

field  value 
prime_id  85584 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /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) [N1/N+1, BrillhartLehmerSelfridge] Reading factors from helper file helper Running N1 test using base 16033 Running N1 test using base 16061 Running N1 test using base 16063 Running N1 test using base 16067 Running N+1 test using discriminant 16103, base 6+sqrt(16103) Calling N1 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]

modified  20081116 12:15:22 
created  20081003 12:01:40 
id  100652 

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
