9 · 21051026 + 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 · 21051026 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):p156 : Murata, Noda, Nohara, NewPGen, MatGFN, PRP, OpenPFGW
Decimal Digits:316392   (log10 is 316391.30646524)
Rank (*):17861 (digit rank is 1)
Entrance Rank (*):61
Currently on list? (*):no
Submitted:12/14/2004 21:14:10 CDT
Last modified:12/14/2004 21:14:10 CDT
Removed (*):11/1/2013 18:27:11 CDT
Database id:72753
Status Flags:none
Score (*):43.0989 (normalized score 0.2236)

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 2415
Subcategory: "Generalized Fermat"
(archival tag id 204734, tag last modified 2022-07-03 08:50:15)

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*2^1051026+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 9*2^1051026+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 116326154 Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(131072,20) to FFT(131072,19) Reduced from FFT(131072,19) to FFT(131072,18) Reduced from FFT(131072,18) to FFT(131072,17) 2102068 bit request FFT size=(131072,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 9*2^1051026+1 is prime! (-2000.8019s+0.0000s)
modified2020-07-07 17:30:45
created2004-12-14 21:23:01

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.