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:

Verification status (*):PRP
Official Comment (*):Lucas cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c46 : Boncompagni, Primo
Decimal Digits:8273   (log10 is 8272.1736326999)
Rank (*):85028 (digit rank is 2)
Entrance Rank (*):58211
Currently on list? (*):no
Submitted:12/23/2011 07:32:51 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:103784
Status Flags:Verify
Score (*):31.852 (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 379
Subcategory: "ECPP"
(archival tag id 214042, tag last modified 2024-07-11 00:37:12)
Lucas cofactor (archivable *)
Prime on list: no, rank 24
Subcategory: "Lucas cofactor"
(archival tag id 214043, tag last modified 2024-04-24 05:37:27)

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.

Bernardo Boncompagni writes (11 May 2021):  (report abuse)
PRIMO certificate: redgolpe.com/L39607.zip

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -o -f -q"V(39607)/158429" 2>&1 PFGW Version [GWNUM 26.5] V(39607)/158429 1/1 mro=0 trial factoring to 2340388 V(39607)/158429 has no small factor. [Elapsed time: 1.788 seconds]
modified2020-07-07 22:30:29
created2011-12-23 07:35:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tc -q"V(39607)/158429" 2>&1 PFGW Version [GWNUM 26.5] Primality testing V(39607)/158429 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 13, base 6+sqrt(13) Calling N-1 BLS with factored part 0.17% and helper 0.06% (0.57% proof) V(39607)/158429 is Fermat and Lucas PRP! (29.2825s+0.0032s) [Elapsed time: 29.00 seconds]
modified2020-07-07 22:30:29
created2011-12-23 07:38:02

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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