7 · 21491852 + 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:7 · 21491852 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(1491851,6)
Proof-code(s): (*):p166 : Yamada, Noda, Nohara, NewPGen, MatGFN, PRP, OpenPFGW
Decimal Digits:449094   (log10 is 449093.04618934)
Rank (*):11781 (digit rank is 1)
Entrance Rank (*):21
Currently on list? (*):no
Submitted:3/2/2005 06:52:42 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:73590
Status Flags:none
Score (*):44.1752 (normalized score 0.4369)

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 Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 22, weight 46.121177924645
Subcategory: "Divides GF(*,6)"
(archival tag id 187054, tag last modified 2023-03-31 01:37:05)

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.
machineWinXP P4 1.8GHz
notesCommand: pfgw.exe -n -f -t -q"7*2^1491852+1" 2>&1 PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 168773583 Running N-1 test using base 3 Primality testing 7*2^1491852+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 7*2^1491852+1 is prime! (45115.8160s+0.0368s)
modified2020-07-07 22:30:44
created2005-03-03 02:42:11

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