3 · 2801978 + 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:3 · 2801978 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(801973,3), GF(801977,5)
Proof-code(s): (*):g372 : Adney, NewPGen, PRP, Proth.exe
Decimal Digits:241420   (log10 is 241419.91098386)
Rank (*):22440 (digit rank is 1)
Entrance Rank (*):123
Currently on list? (*):no
Submitted:9/2/2005 01:09:08 CDT
Last modified:9/2/2005 06:50:02 CDT
Database id:75498
Status Flags:none
Score (*):42.2673 (normalized score 0.1117)

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 29, weight 43.365949223547
Subcategory: "Divides GF(*,5)"
(archival tag id 187123, tag last modified 2020-10-29 19:20:16)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 30, weight 43.365949223547
Subcategory: "Divides GF(*,3)"
(archival tag id 187122, tag last modified 2021-02-26 11:20:20)

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.
fieldvalue
prime_id75498
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -f -t -q"3*2^801978+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3*2^801978+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 87243490 Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) 1603968 bit request FFT size=(98304,17) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^801978+1 is prime! (11949.1881s+0.0107s) [Elapsed time: 11949 seconds]
modified2020-07-07 17:30:43
created2005-09-02 01:23:00
id80665

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