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 (*):Euler irregular, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c8 : Broadhurst, Water, Primo
Decimal Digits:9516   (log10 is 9515.9812816038)
Rank (*):81842 (digit rank is 1)
Entrance Rank (*):67840
Currently on list? (*):short
Submitted:6/21/2014 18:10:51 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:118067
Blob database id:327
Status Flags:Verify
Score (*):32.2863 (normalized score 0)

Description: (from blob table id=327)

[This prime has a pre-calculated decimal expansion (linked blob)]

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.
Euler Irregular primes (archivable *)
Prime on list: yes, rank 7
Subcategory: "Euler Irregular primes"
(archival tag id 217725, tag last modified 2023-05-12 22:37:14)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 320
Subcategory: "ECPP"
(archival tag id 217726, tag last modified 2023-09-17 09:37:11)

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)

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.
machineWinXP Dual Core 2.6GHz 64-bit Laptop
notesCommand: pfgw64.exe -tc p_118067.txt 2>&1 PFGW Version [GWNUM 27.8] Primality testing 9578149333...8683176273 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 10+sqrt(13) Calling N-1 BLS with factored part 0.11% and helper 0.03% (0.35% proof) 9578149333...8683176273 is Fermat and Lucas PRP! (26.6857s+0.1862s) [Elapsed time: 27 seconds]
modified2020-07-07 22:30:17
created2014-06-21 18:35:15

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.
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