118442328862282459012925328173493478126787291226668192 + 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.

118442328862282459012925328173493478126787291226668192 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):p417 : Tennant, LLR2, PrivGfnServer, OpenPFGW
Decimal Digits:1000000   (log10 is 999999)
Rank (*):1139 (digit rank is 13)
Entrance Rank (*):1005
Currently on list? (*):short
Submitted:5/2/2021 04:01:32 CDT
Last modified:5/2/2021 21:52:51 CDT
Database id:132271
Status Flags:TrialDiv
Score (*):46.633 (normalized score 8.9153)

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 330
Subcategory: "Generalized Fermat"
(archival tag id 226102, tag last modified 2021-10-22 02:37:18)

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)) + 234425)^8192 + 1

Private GFN server writes (2 May 2021):  (report abuse)
To prove with PFGW, use "factor helper file" with following content (two largest factors of the base):


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...8729122666^8192+1 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper_file_id_132271 Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 89.10% 1175412837...8729122666^8192+1 is prime! (24527.0779s+0.0118s) [Elapsed time: 6.81 hours] Helper File: 2 7523 1352449169 57762824434344582535778429685105848...(109 digits)...63544378365496224267118391042849559
modified2021-05-03 13:39:09
created2021-05-02 15:04:04

Query times: 0.0006 seconds to select prime, 0.0008 seconds to seek comments.
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