815730721 · 22095440 + 1

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:815730721 · 22095440 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L466 : Zhou, NewPGen, LLR
Decimal Digits:630800   (log10 is 630799.20566095)
Rank (*):3687 (digit rank is 1)
Entrance Rank (*):1373
Currently on list? (*):yes
Submitted:3/15/2019 16:08:08 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:126314
Status Flags:TrialDiv
Score (*):45.2187 (normalized score 1.5716)

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.
Generalized Fermat (archivable *)
Prime on list: no, rank 937
Subcategory: "Generalized Fermat"
(archival tag id 220177, tag last modified 2023-03-21 08:37:20)

User comments about this prime (disclaimer):

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Lei Zhou writes (15 Mar 2019):  (report abuse)
815730721*2^2095440+1 is a Generalized Fermat Prime.

815730721*2^2095440+1 = (13*2^261930)^8+1

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"815730721*2^2095440+1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 815730721*2^2095440+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 815730721*2^2095440+1 is prime! (2725.1668s+0.0010s) [Elapsed time: 45.43 minutes]
modified2020-07-07 22:30:13
created2019-03-15 16:11:01

Query times: 0.0018 seconds to select prime, 0.0006 seconds to seek comments.
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