400254 · 127400254 + 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:400254 · 127400254 + 1
Verification status (*):Proven
Official Comment (*):Generalized Cullen
Proof-code(s): (*):g407 : HermleGC, MultiSieve, PRP, Proth.exe
Decimal Digits:842062   (log10 is 842061.45686319)
Rank (*):3415 (digit rank is 1)
Entrance Rank (*):103
Currently on list? (*):short
Submitted:6/4/2013 03:32:55 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:114324
Status Flags:none
Score (*):46.1055 (normalized score 2.9572)

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 27
Subcategory: "Generalized Cullen"
(archival tag id 217180, tag last modified 2023-12-29 19:37:13)

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 400254 127 400254 1 2>&1 [Elapsed time: 9.674 seconds]
modified2020-07-07 22:30:19
created2013-06-04 03:35:02

machineWinXP Dual Core 2.6GHz 64-bit Laptop
notesCommand: pfgw64.exe -t -q"400254*127^400254+1" 2>&1 PFGW Version [GWNUM 27.8] Primality testing 400254*127^400254+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 400254*127^400254+1 is prime! (9832.4878s+0.0405s) [Elapsed time: 9834 seconds]
modified2020-07-07 22:30:19
created2013-06-04 13:04:29

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.