11754128376394782080351\
49360635999371658705159870633484377238553812244526\
118442328862282459012925328173493478126787290237868192 + 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\
118442328862282459012925328173493478126787290237868192 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):p416 : Monnin, LLR2, PrivGfnServer, OpenPFGW
Decimal Digits:1000000   (log10 is 999999)
Rank (*):2894 (digit rank is 17)
Entrance Rank (*):985
Currently on list? (*):yes
Submitted:4/6/2021 18:32:23 UTC
Last modified:6/10/2023 03:37:14 UTC
Database id:132212
Status Flags:none
Score (*):46.633 (normalized score 4.4938)

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 1180
Subcategory: "Generalized Fermat"
(archival tag id 226081, tag last modified 2024-11-23 21:37:10)

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.

Private GFN server writes (6 Apr 2021):  (report abuse)
To prove it with PFGW, use "Factor Helper File" (-h option). The base was factorized using YAFU. Two largest factors (which should be put into this file) are: 102934239816486361102607080101997899898038675281 and 473777469634854139236065334735086157108209901510149

Jeppe Stig Nielsen writes (10 Apr 2021):  (report abuse)
Can be written more compactly as: 
(floor(10^(999999/8192)) + 135545)^8192 + 1
FactorDB has the factorization of the base mentioned in the user comment by Private GFN server.

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_id132212
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesPFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 1175412837...8729023786^8192+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file p_132212
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 41.51%


1175412837...8729023786^8192+1 is prime! (57524.7720s+0.0104s)
[Elapsed time: 15.98 hours]


Helper File:
102934239816486361102607080101997899898038675281
473777469634854139236065334735086157108209901510149
modified2023-06-10 03:37:14
created2023-06-09 11:38:29
id181981

fieldvalue
prime_id132212
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...8729023786^8192+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 5.53% 1175412837...8729023786^8192+1 is PRP! (45003.2256s+0.1739s) [Elapsed time: 12.50 hours]
modified2021-04-20 22:39:24
created2021-04-06 18:36:01
id177911

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