11754128376394782080351\
49360635999371658705159870633484377238553812244526\
118442328862282459012925328173493478126787295998648192 + 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:

Description:11754128376394782080351\
49360635999371658705159870633484377238553812244526\
118442328862282459012925328173493478126787295998648192 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L5749 : Gahan, LLR2, LLR
Decimal Digits:1000000   (log10 is 999999)
Rank (*):2869 (digit rank is 12)
Entrance Rank (*):2117
Currently on list? (*):short
Submitted:6/2/2023 12:38:30 UTC
Last modified:6/7/2023 04:17:35 UTC
Database id:136122
Status Flags:none
Score (*):46.633 (normalized score 4.5827)

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 1162
Subcategory: "Generalized Fermat"
(archival tag id 228608, tag last modified 2024-10-29 10:37:19)

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 (3 Jun 2023):  (report abuse)
The 123-digit base is 8 times a 122-digit number. Prove that the 122-digit number is prime and put it in the PFGW helper file.

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_id136122
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesPFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 1175412837...8729599864^8192+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file p_136122
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 99.26%


1175412837...8729599864^8192+1 is prime! (27502.1942s+0.0162s)
[Elapsed time: 7.64 hours]


Helper File:
14692660470493477600439367007949992...(122 digits)...30737661566602168668476584841199983
modified2023-06-07 04:17:35
created2023-06-06 20:39:13
id181970

fieldvalue
prime_id136122
person_id9
machineUsing: Digital Ocean Droplet
whatprp
notesPFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 1175412837...8729599864^8192+1 [N-1, Brillhart-Lehmer-Selfridge]
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 0.74%


1175412837...8729599864^8192+1 is PRP! (30048.3221s+0.0103s)
[Elapsed time: 8.35 hours]
modified2023-06-03 12:52:03
created2023-06-03 04:31:15
id181952

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