21 · 21421741 + 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:21 · 21421741 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):g279 : Cooper, NewPGen, PRP, Proth.exe
Decimal Digits:427989   (log10 is 427988.0092846)
Rank (*):12536 (digit rank is 1)
Entrance Rank (*):20
Currently on list? (*):no
Submitted:1/18/2005 23:08:09 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):8/16/2019 21:19:40 UTC
Database id:73190
Status Flags:none
Score (*):44.0273 (normalized score 0.3905)

User comments about this prime (disclaimer):

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Curtis Cooper writes (11 Sep 2014):  (report abuse)
21*2^1421741+1 is a Factor of GF(1421740,11)
21*2^1421741+1 is a Factor of xGF(1421740,12,5)

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_id73190
person_id9
machineWinXP P4 1.8GHz
whatprime
notesCommand: pfgw.exe -n -f -t -q"21*2^1421741+1" 2>&1 PFGW Version 20030811.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 160363099 Running N-1 test using base 5 N-1: 21*2^1421741+1Primality testing 21*2^1421741+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 21*2^1421741+1 is prime! (44302.9132s+0.0556s)
modified2020-07-07 22:30:44
created2005-01-19 04:01:13
id78203

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