118442328862282459012925328173493478126787293753508192 + 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.

118442328862282459012925328173493478126787293753508192 + 1
Verification status (*):PRP
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 (*):1136 (digit rank is 10)
Entrance Rank (*):1044
Currently on list? (*):short
Submitted:6/15/2021 12:40:04 CDT
Last modified:6/15/2021 20:37:17 CDT
Database id:132402
Status Flags:Verify, TrialDiv
Score (*):46.633 (normalized score 8.9142)

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 327
Subcategory: "Generalized Fermat"
(archival tag id 226152, 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)) + 487109)^8192 + 1

Private GFN server writes (15 Jun 2021):  (report abuse)
Base factorized using YAFU. To prove as prime, use PFGW "factor helper file" with following factors:
(remaining factors are 2*5*5, they're not important for PFGW)

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...8729375350^8192+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 1.39%

1175412837...8729375350^8192+1 is PRP! (26428.7211s+0.0788s)
[Elapsed time: 7.34 hours]
modified2021-06-15 20:01:30
created2021-06-15 12:41:01

Query times: 0.0005 seconds to select prime, 0.0009 seconds to seek comments.
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