1381595338887690358821474589959638055848096769928148782339849168699728696005036217596639028980911635464344630906955931847649826418753025466730960\
47093511481998019892105889132464543550102310865144\
502037206654116795191514099734330521220120978751444096 + 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:1381595338887690358821474589959638055848096769928148782339849168699728696005036217596639028980911635464344630906955931847649826418753025466730960\
47093511481998019892105889132464543550102310865144\
502037206654116795191514099734330521220120978751444096 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):p421 : Gahan, LLR2, PrivGfnServer, OpenPFGW
Decimal Digits:1000000   (log10 is 999999)
Rank (*):2916 (digit rank is 18)
Entrance Rank (*):1089
Currently on list? (*):yes
Submitted:8/15/2021 20:44:31 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:132621
Status Flags:none
Score (*):46.633 (normalized score 4.3766)

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 1198
Subcategory: "Generalized Fermat"
(archival tag id 226262, tag last modified 2024-12-13 10:37:10)

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 (15 Aug 2021):  (report abuse)
Factors of the base for PFGW factor helper file. Factorized using YAFU (ECM phase)
2
6659
517873
18061074341
682329797
40636909434679161566151110451715104843939797744362951490557714577937371022604869669885587175874687571414955559444176932616196836944503080748787069831602317238891081922897238012052078727985063912631423873224244374587

Jeppe Stig Nielsen writes (13 Nov 2021):  (report abuse)
Can be written more compactly as:
(floor(10^(999999/4096)) + 136686)^4096 + 1

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_id132621
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesPFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 1381595338...2097875144^4096+1 [N-1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_file_id_132621
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 87.90%


1381595338...2097875144^4096+1 is prime! (46389.9228s+0.0273s)
[Elapsed time: 12.89 hours]
Helper file contains: "18061074341,682329797,40636909434679161566151110451715104843939797744362951490557714577937371022604869669885587175874687571414955559444176932616196836944503080748787069831602317238891081922897238012052078727985063912631423873224244374587"
modified2023-03-16 23:00:51
created2023-03-16 10:07:41
id181606

fieldvalue
prime_id132621
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesPFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 1381595338...2097875144^4096+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 4.28% 1381595338...2097875144^4096+1 is PRP! (25200.6712s+0.0117s) [Elapsed time: 7.00 hours]
modified2022-07-11 18:21:46
created2021-08-15 20:46:01
id178333

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