V(49391)/298414424560419239
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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:V(49391)/298414424560419239
Verification status (*):PRP
Official Comment:Lucas cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Water, Broadhurst, Primo
Decimal Digits:10305   (log10 is 10304.633719775)
Rank (*):72657 (digit rank is 1)
Entrance Rank (*):63613
Currently on list? (*):short
Submitted:6/16/2013 09:48:33 CDT
Last modified:6/16/2013 10:20:26 CDT
Database id:114432
Status Flags:Verify
Score (*):32.5331 (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 147
Subcategory: "ECPP"
(archival tag id 217185, tag last modified 2017-11-16 23:50:19)
Lucas cofactor (archivable *)
Prime on list: yes, rank 7
Subcategory: "Lucas cofactor"
(archival tag id 217186, tag last modified 2015-03-12 17:20:33)

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.

David Broadhurst writes (11 Sep 2014): 
certificate

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_id114432
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"V(49391)/298414424560419239" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
V(49391)/298414424560419239 1/1 mro=0


trial factoring to 2968100
V(49391)/298414424560419239 has no small factor.
[Elapsed time: 2.761 seconds]
modified2013-08-16 09:44:46
created2013-06-16 09:52:02
id159242

fieldvalue
prime_id114432
person_id9
machineRedHat P4 P4
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"V(49391)/298414424560419239" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing V(49391)/298414424560419239 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N-1 BLS with factored part 0.11% and helper 0.00% (0.35% proof)
V(49391)/298414424560419239 is Fermat and Lucas PRP! (53.2562s+0.0042s)
[Elapsed time: 53.00 seconds]
modified2013-08-16 09:44:46
created2013-06-16 09:53:01
id159243

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