Phi(561, 43669)/361212114583
(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:Phi(561, 43669)/361212114583
Verification status (*):PRP
Official Comment:ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c13 : Steward, OpenPFGW, Primo
Decimal Digits:10472   (log10 is 10471.883384047)
Rank (*):72469 (digit rank is 1)
Entrance Rank (*):51872
Currently on list? (*):no
Submitted:3/20/2011 08:29:22 CDT
Last modified:3/20/2011 12:39:56 CDT
Database id:99246
Status Flags:Verify
Score (*):32.583 (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 138
Subcategory: "ECPP"
(archival tag id 213174, tag last modified 2017-10-14 12:20:20)

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.

Andrew A. D. Steward writes (11 Sep 2014): 
Primo certificate at http://www.primes.viner-steward.org/andy/D/110E2773.zip Single core.

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_id99246
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"Phi(561,4366^9)/361212114583" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Phi(561,4366^9)/361212114583 1/1 mro=0


trial factoring to 3020139
Phi(561,4366^9)/361212114583 has no small factor.
[Elapsed time: 2.871 seconds]
modified2011-12-27 16:48:33
created2011-03-20 08:35:01
id127879

fieldvalue
prime_id99246
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"Phi(561,4366^9)/361212114583" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing Phi(561,4366^9)/361212114583 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 11, base 2+sqrt(11)
Calling N-1 BLS with factored part 0.11% and helper 0.06% (0.38% proof)
Phi(561,4366^9)/361212114583 is Fermat and Lucas PRP! (53.8338s+0.0028s)
[Elapsed time: 54.00 seconds]
modified2011-03-25 10:27:28
created2011-03-20 08:36:13
id127882

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