81 · 21643428 + 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:81 · 21643428 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):g418 : Taura, NewPGen, PRP, Proth.exe
Decimal Digits:494724   (log10 is 494723.03219909)
Rank (*):3597 (digit rank is 1)
Entrance Rank (*):88
Currently on list? (*):yes
Submitted:3/6/2009 17:53:42 CDT
Last modified:3/6/2009 23:50:20 CDT
Database id:87009
Status Flags:none
Score (*):44.4725 (normalized score 1.3149)

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 985
Subcategory: "Generalized Fermat"
(archival tag id 208929, tag last modified 2020-08-02 04:20:11)

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_id87009
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 81 2 1643428 1 2>&1 [Elapsed time: 10.077 seconds]
modified2020-07-07 17:30:38
created2009-03-06 18:05:01
id103387

fieldvalue
prime_id87009
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"81*2^1643428+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 81*2^1643428+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3286878 bit request FFT size=(229376,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 81*2^1643428+1 is prime! (19425.1235s+0.0014s) [Elapsed time: 5.40 hours]
modified2020-07-07 17:30:38
created2009-03-06 18:08:02
id103388

Query times: 0.0005 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.