11754128376394782080351\
49360635999371658705159870633484377238553812244526\
118442328862282459012925328173493478126787293753508192 + 1

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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:11754128376394782080351\
49360635999371658705159870633484377238553812244526\
118442328862282459012925328173493478126787293753508192 + 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 (*):2889 (digit rank is 13)
Entrance Rank (*):1044
Currently on list? (*):yes
Submitted:6/15/2021 17:40:04 UTC
Last modified:6/8/2023 11:42:56 UTC
Database id:132402
Status Flags:none
Score (*):46.633 (normalized score 4.5047)

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 1175
Subcategory: "Generalized Fermat"
(archival tag id 226152, tag last modified 2024-11-22 05:37:10)

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:
7436070673651
9735020690542051687514731015890685180257085700171
32474317895301702700927846996187126772949250093437843108067
(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.
fieldvalue
prime_id132402
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesPFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 1175412837...8729375350^8192+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file p_132402
trial


Running N-1 test using base 3
Generic modular reduction using generic reduction FMA3 FFT length 336K, Pass1=448, Pass2=768, clm=4 on A 3321925-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 47.93%


1175412837...8729375350^8192+1 is prime! (37978.0055s+0.0091s)
[Elapsed time: 10.55 hours]


Helper File:
7436070673651
9735020690542051687514731015890685180257085700171
32474317895301702700927846996187126772949250093437843108067
modified2023-06-08 11:42:56
created2023-06-08 01:09:57
id181975

fieldvalue
prime_id132402
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesPFGW Version 4.0.1.64BIT.20191203.x86_Dev [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]
modified2022-07-11 18:21:46
created2021-06-15 17:41:01
id178114

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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