11754128376394782080351\
49360635999371658705159870633484377238553812244526\
118442328862282459012925328173493478126787292400928192 + 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.

Description:11754128376394782080351\
49360635999371658705159870633484377238553812244526\
118442328862282459012925328173493478126787292400928192 + 1
Verification status (*):PRP
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):p419 : Bird1, LLR2, PrivGfnServer, OpenPFGW
Decimal Digits:1000000   (log10 is 999999)
Rank (*):1109 (digit rank is 11)
Entrance Rank (*):1014
Currently on list? (*):short
Submitted:5/10/2021 01:37:31 CDT
Last modified:5/10/2021 09:37:17 CDT
Database id:132307
Status Flags:Verify, TrialDiv
Score (*):46.633 (normalized score 9.0656)

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 324
Subcategory: "Generalized Fermat"
(archival tag id 226110, tag last modified 2021-09-05 19:37:18)

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)) + 351851)^8192 + 1

Private GFN server writes (10 May 2021):  (report abuse)
Largest factors of the base for PFGW "factor helper file":
1162969
1405249
32260609
78653214047
131884894427890965255992540243324672347259028010130723261188820316992513123101785236491

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_id132307
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...8729240092^8192+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 20.52% 1175412837...8729240092^8192+1 is PRP! (25315.6054s+0.0977s) [Elapsed time: 7.03 hours]
modified2021-05-14 12:47:21
created2021-05-10 01:41:02
id178019

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.
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