Phi(741, - 638479)/44250132909040111
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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(741, - 638479)/44250132909040111
Verification status (*):PRP
Official Comment:ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c54 : Wu_T, Primo
Decimal Digits:18666   (log10 is 18665.740332862)
Rank (*):65336 (digit rank is 1)
Entrance Rank (*):55717
Currently on list? (*):no
Submitted:5/11/2013 03:17:05 CDT
Last modified:5/11/2013 03:50:28 CDT
Database id:114110
Status Flags:Verify
Score (*):34.3727 (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 27
Subcategory: "ECPP"
(archival tag id 217143, tag last modified 2017-11-16 23:50:19)

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.

Tom Wu writes (11 Sep 2014): 
This prime is a helper for the N-1 primality proof of the GRU prime Phi(13339,63847), and can also be expressed as Phi(13338,63847)/44250132909040111.

The Primo certificate is available from

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(741,-63847^9)/44250132909040111" 2>&1
PFGW Version [GWNUM 26.5]
Phi(741,-63847^9)/44250132909040111 1/1 mro=0

trial factoring to 5634268
Phi(741,-63847^9)/44250132909040111 has no small factor.
[Elapsed time: 9.438 seconds]
modified2013-06-04 07:30:39
created2013-05-11 03:20:03

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"Phi(741,-63847^9)/44250132909040111" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing Phi(741,-63847^9)/44250132909040111 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 7, base 9+sqrt(7)
Calling N-1 BLS with factored part 0.06% and helper 0.04% (0.23% proof)
Phi(741,-63847^9)/44250132909040111 is Fermat and Lucas PRP! (133.5777s+0.0060s)
[Elapsed time: 2.23 minutes]
modified2013-06-04 07:30:39
created2013-05-11 03:38:01

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.