3 · 22478785 + 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:3 · 22478785 + 1
Verification status (*):Proven
Official Comment (*):Divides Fermat F(2478782), GF(2478782,3), GF(2478776,6), GF(2478782,12)
Proof-code(s): (*):g245 : Cosgrave, NewPGen, PRP, Proth.exe
Decimal Digits:746190   (log10 is 746189.1149232)
Rank (*):3865 (digit rank is 1)
Entrance Rank (*):7
Currently on list? (*):short
Submitted:10/14/2003 14:15:38 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:66628
Status Flags:none
Score (*):45.7345 (normalized score 2.0233)

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: yes, rank 15, weight 46.833134066262
Subcategory: "Divides GF(*,12)"
(archival tag id 187025, tag last modified 2024-07-09 23:37:24)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 12, weight 46.833134066262
Subcategory: "Divides GF(*,6)"
(archival tag id 187024, tag last modified 2023-03-31 01:37:05)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: yes, rank 16, weight 46.833134066262
Subcategory: "Divides GF(*,3)"
(archival tag id 187023, tag last modified 2024-03-22 08:37:11)
Fermat Divisors (archivable *)
Prime on list: yes, rank 9, weight 46.833134066262
Subcategory: "Divides Fermat"
(archival tag id 187022, tag last modified 2023-07-18 02:37:34)

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"3*2^2478785+1" 2>&1 PFGW Version 20030811.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 289235494 Running N-1 test using base 5 Primality testing 3*2^2478785+1 [N-1, Brillhart-Lehmer-Selfridge] Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(327680,19) to FFT(327680,18) Reduced from FFT(327680,18) to FFT(327680,17) Reduced from FFT(327680,17) to FFT(327680,16) 4957582 bit request FFT size=(327680,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^2478785+1 is prime! (126155.4235s+0.0018s)
modified2020-07-07 22:30:47
created2003-10-14 14:23:01

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
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