U(42043)/1681721
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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:U(42043)/1681721
Verification status (*):PRP
Official Comment:Fibonacci cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c56 : Soule, Minovic, OpenPFGW, Primo
Decimal Digits:8780   (log10 is 8779.8921200803)
Rank (*):74066 (digit rank is 2)
Entrance Rank (*):58422
Currently on list? (*):short
Submitted:2/21/2012 20:31:42 CDT
Last modified:2/21/2012 22:24:18 CDT
Database id:104907
Status Flags:Verify
Score (*):32.0367 (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 189
Subcategory: "ECPP"
(archival tag id 214059, tag last modified 2017-10-14 12:20:20)
Fibonacci cofactor (archivable *)
Prime on list: yes, rank 9
Subcategory: "Fibonacci cofactor"
(archival tag id 214060, tag last modified 2017-04-14 17:50:17)

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.

Predrag Minovic writes (11 Sep 2014): 
The certificate can be found here.

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_id104907
person_id9
machineRedHat Virtual STEM Server
whatprp
notesCommand: /home/caldwell/client/pfgw -tc -q"U(42043)/1681721" 2>&1
PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14]
Primality testing U(42043)/1681721 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 8+sqrt(13)
Calling N+1 BLS with factored part 0.09% and helper 0.01% (0.29% proof)
U(42043)/1681721 is Fermat and Lucas PRP! (18.6512s+0.2016s)
[Elapsed time: 28.00 seconds]
modified2012-07-16 11:33:02
created2012-02-21 20:33:19
id139398

fieldvalue
prime_id104907
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"U(42043)/1681721" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
U(42043)/1681721 1/1 mro=0


trial factoring to 2496234
U(42043)/1681721 has no small factor.
[Elapsed time: 2.236 seconds]
modified2012-07-16 11:33:02
created2012-02-21 22:24:15
id139431

Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.