118442328862282459012925328173493478126787291546788192 + 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:

118442328862282459012925328173493478126787291546788192 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p418 : Sielemann, LLR2, PrivGfnServer, OpenPFGW
Decimal Digits:1000000   (log10 is 999999)
Rank (*):2581 (digit rank is 15)
Entrance Rank (*):1005
Currently on list? (*):short
Submitted:5/2/2021 09:14:01 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:132272
Status Flags:none
Score (*):46.633 (normalized score 5.426)

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 985
Subcategory: "Generalized Fermat"
(archival tag id 226103, tag last modified 2024-03-01 23:37:20)

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.

Jeppe Stig Nielsen writes (8 Aug 2021):  (report abuse)
Can be written more compactly as:
(floor(10^(999999/8192)) + 266437)^8192 + 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 (pool) 4c+4c 3.5GHz
notesPFGW Version [GWNUM 29.8] Primality testing 1175412837...8729154678^8192+1 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_file_id_132272 Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 99.75% 1175412837...8729154678^8192+1 is prime! (25962.8083s+0.0117s) [Elapsed time: 7.21 hours] Helper File: 2 58770641881973910401757468031799968...(122 digits)...22950646266408674673906339364577339
modified2021-05-03 18:39:09
created2021-05-03 11:25:30

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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