V(31547)/221409808384144085062492986575402586918348866650893130934479823303462\
27824686184228977375762399380559492255026457207263\
13249552565534024996670996378968020508259098756301

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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(31547)/221409808384144085062492986575402586918348866650893130934479823303462\
27824686184228977375762399380559492255026457207263\
13249552565534024996670996378968020508259098756301
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:6425   (log10 is 6424.58789011)
Rank (*):77897 (digit rank is 1)
Entrance Rank (*):68709
Currently on list? (*):short
Submitted:6/25/2013 22:34:36 CDT
Last modified:6/26/2013 00:50:28 CDT
Database id:114487
Status Flags:Verify
Score (*):31.0677 (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 294
Subcategory: "ECPP"
(archival tag id 217192, tag last modified 2017-11-27 10:20:19)
Lucas cofactor (archivable *)
Prime on list: yes, rank 16
Subcategory: "Lucas cofactor"
(archival tag id 217193, 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_id114487
person_id9
machineDitto P4 P4
whattrial_divided
notesPFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
V(31547)/2214098....0508259098756301 1/1 mro=0


trial factoring to 1779944
V(31547)/2214098083...9098756301 has no small factor.
[Elapsed time: 2.551 seconds]
modified2013-08-16 09:44:45
created2013-06-25 22:35:02
id159352

fieldvalue
prime_id114487
person_id9
machineWinXP Dual Core 2.6GHz 64-bit Laptop
whatprp
notesPFGW Version 3.7.3.64BIT.20130210.Win_Dev [GWNUM 27.8]
Primality testing V(31547)/2214098083...9098756301 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 7, base 2+sqrt(7)
Calling N+1 BLS with factored part 0.18% and helper 0.15% (0.69% proof)
V(31547)/2214098083...9098756301 is Fermat and Lucas PRP! (3.7093s+0.0202s)
[Elapsed time: 4 seconds]
modified2013-08-16 09:44:45
created2013-06-26 00:33:23
id159353

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.