729 · 2554074 + 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:729 · 2554074 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L656 : Yama, Srsieve, PrimeGrid, LLR
Decimal Digits:166796   (log10 is 166795.75654505)
Rank (*):35238 (digit rank is 1)
Entrance Rank (*):1546
Currently on list? (*):no
Submitted:2/25/2009 01:45:36 CDT
Last modified:2/25/2009 02:20:20 CDT
Removed (*):10/5/2010 13:32:28 CDT
Database id:86871
Status Flags:none
Score (*):41.1296 (normalized score 0.0301)

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 2668
Subcategory: "Generalized Fermat"
(archival tag id 208922, tag last modified 2022-09-24 15:50:10)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 729 2 554074 1 2>&1 [Elapsed time: 9.680 seconds]
modified2020-07-07 17:30:38
created2009-02-25 01:48:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"729*2^554074+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 729*2^554074+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(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) 1108176 bit request FFT size=(65536,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 729*2^554074+1 is prime! (1472.1600s+0.0000s) [Elapsed time: 24.67 minutes]
modified2020-07-07 17:30:38
created2009-02-25 01:53:01

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.