V(25763)/92864275685263243511877732271066626563444291249

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly.  This list is the most important PrimePages database: 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:

Description:V(25763)/92864275685263243511877732271066626563444291249
Verification status (*):PRP
Official Comment (*):Lucas cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:5338   (log10 is 5337.1807270845)
Rank (*):90283 (digit rank is 11)
Entrance Rank (*):70478
Currently on list? (*):no
Submitted:5/23/2013 20:21:30 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:114222
Status Flags:Verify
Score (*):30.4919 (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 530
Subcategory: "ECPP"
(archival tag id 217164, tag last modified 2024-03-24 06:37:14)
Lucas cofactor (archivable *)
Prime on list: no, rank 30
Subcategory: "Lucas cofactor"
(archival tag id 217165, tag last modified 2023-11-19 12:37:21)

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):  (report abuse)
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_id114222
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"V(25763)/92864275685263243511877732271066626563444291249" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] V(25763)/9286427....6626563444291249 1/1 mro=0 trial factoring to 1455600 V(25763)/9286427568...3444291249 has no small factor. [Elapsed time: 0.757 seconds]
modified2020-07-07 22:30:19
created2013-05-23 20:35:02
id158822

fieldvalue
prime_id114222
person_id9
machineDitto P4 P4
whatprp
notesCommand: /home/ditto/client/pfgw -tc -q"V(25763)/92864275685263243511877732271066626563444291249" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing V(25763)/9286427568...3444291249 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N+1 test using discriminant 29, base 1+sqrt(29) Calling N+1 BLS with factored part 0.33% and helper 0.17% (1.19% proof) V(25763)/9286427568...3444291249 is Fermat and Lucas PRP! (9.9668s+0.0020s) [Elapsed time: 10.00 seconds]
modified2020-07-07 22:30:19
created2013-05-23 20:38:08
id158827

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