Phi(5161, - 100)
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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(5161, - 100)
Verification status (*):PRP
Official Comment:Unique, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c47 : Chandler, Primo
Decimal Digits:9505   (log10 is 9504.00432137378)
Rank (*):74235 (digit rank is 2)
Entrance Rank (*):62586
Currently on list? (*):short
Submitted:12/14/2012 14:15:46 CDT
Last modified:12/14/2012 14:50:25 CDT
Database id:110404
Status Flags:Verify
Score (*):32.2824 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 186
Subcategory: "ECPP"
(archival tag id 214821, tag last modified 2018-07-16 18:20:22)
Unique (archivable *)
Prime on list: yes, rank 9
Subcategory: "Unique"
(archival tag id 214822, tag last modified 2014-05-20 07:51:28)

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.

Ray Chandler writes (11 Sep 2014): 
certificate verified

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f -q"Phi(5161,-100)" 2>&1
PFGW Version [GWNUM 26.5]
Phi(5161,-100) 1/1 mro=0

trial factoring to 2719581
Phi(5161,-100) has no small factor.
[Elapsed time: 9.403 seconds]
modified2012-12-19 19:14:49
created2012-12-14 14:18:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"Phi(5161,-100)" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing Phi(5161,-100) [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 31
Calling Brillhart-Lehmer-Selfridge with factored part 0.99%
Phi(5161,-100) is PRP! (17.2999s+0.0009s)
[Elapsed time: 17.00 seconds]
modified2012-12-19 19:14:49
created2012-12-14 14:23:01

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.