459 · 2816031 + 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:459 · 2816031 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(816030,5)
Proof-code(s): (*):L1498 : Goral, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:245653   (log10 is 245652.47020436)
Rank (*):21811 (digit rank is 1)
Entrance Rank (*):1237
Currently on list? (*):no
Submitted:2/12/2011 18:27:51 CDT
Last modified:2/13/2011 05:50:24 CDT
Database id:98341
Status Flags:none
Score (*):42.3207 (normalized score 0.1215)

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 27, weight 48.449840215409
Subcategory: "Divides GF(*,5)"
(archival tag id 213126, tag last modified 2020-10-29 19:20:16)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 459 2 816031 1 2>&1 [Elapsed time: 10.330 seconds]
modified2020-07-07 17:30:32
created2011-02-12 18:35:53

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"459*2^816031+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 459*2^816031+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 459*2^816031+1 is prime! (-718.9973s+0.0000s) [Elapsed time: 60.82 minutes]
modified2020-07-07 17:30:32
created2011-02-13 04:29:24

Query times: 0.0004 seconds to select prime, 0.0009 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.