9 · 2461081 + 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:9 · 2461081 + 1
Verification status (*):Proven
Official Comment (*):Divides Fermat F(461076), GF(461077,3), GF(461077,6), GF(461077,12)
Proof-code(s): (*):g122 : Nohara, Proth.exe
Decimal Digits:138801   (log10 is 138800.16567325)
Rank (*):39467 (digit rank is 1)
Entrance Rank (*):132
Currently on list? (*):no
Submitted:8/5/2003 09:49:56 CDT
Last modified:8/5/2003 09:49:56 CDT
Database id:65770
Status Flags:none
Score (*):40.564 (normalized score 0.0177)

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 31, weight 42.76131105727
Subcategory: "Divides GF(*,12)"
(archival tag id 187433, tag last modified 2022-04-12 17:37:10)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 32, weight 42.76131105727
Subcategory: "Divides GF(*,6)"
(archival tag id 187432, tag last modified 2022-05-12 21:37:21)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 40, weight 42.76131105727
Subcategory: "Divides GF(*,3)"
(archival tag id 187431, tag last modified 2021-02-26 11:20:20)
Fermat Divisors (archivable *)
Prime on list: no, rank 25, weight 42.76131105727
Subcategory: "Divides Fermat"
(archival tag id 187430, tag last modified 2021-01-16 15:20:20)

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.
machineLinux P4 2.8GHz
notesCommand: /home/caldwell/client/pfgw -f -t -q"9*2^461081+1" 2>&1 PFGW Version 20030702.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 48372670 Running N-1 test using base 11 Primality testing 9*2^461081+1 [N-1, Brillhart-Lehmer-Selfridge] Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) 922178 bit request FFT size=(57344,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 9*2^461081+1 is prime! (1624.0600s+0.0000s)
modified2020-07-07 17:30:47
created2003-08-05 09:59:07

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.