1740349 · 23480698 + 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:1740349 · 23480698 + 1
Verification status (*):Proven
Official Comment (*):Generalized Cullen
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L5765 : Propper, Gcwsieve, LLR
Decimal Digits:1047801   (log10 is 1047800.744484)
Rank (*):1687 (digit rank is 1)
Entrance Rank (*):1164
Currently on list? (*):short
Submitted:7/6/2023 11:28:40 UTC
Last modified:7/6/2023 14:37:19 UTC
Database id:136235
Status Flags:none
Score (*):46.7762 (normalized score 5.7975)

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 Cullen (archivable *)
Prime on list: no, rank 21
Subcategory: "Generalized Cullen"
(archival tag id 228684, tag last modified 2023-12-29 19:37:13)

User comments about this prime (disclaimer):

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Jeppe Stig Nielsen writes (7 Jul 2023):  (report abuse)
Of course, 1740349*2^3480698 + 1 = 1740349*4^1740349 + 1 (so Cullen base 4).

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.
machineUsing: Digital Ocean Droplet
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -t -q"1740349*2^3480698+1" 2>&1
PFGW Version [GWNUM 30.11]
Primality testing 1740349*2^3480698+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 3
Special modular reduction using zero-padded FMA3 FFT length 384K, Pass1=384, Pass2=1K, clm=4 on 1740349*2^3480698+1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%

1740349*2^3480698+1 is prime! (10005.3795s+0.0016s)
[Elapsed time: 2.78 hours]
modified2023-07-06 14:15:47
created2023-07-06 11:29:02

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