3 · 2709968 + 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 · 2709968 + 1
Verification status (*):Proven
Official Comment (*):Divides GF(709962,3), GF(709963,5)
Proof-code(s): (*):g372 : Adney, NewPGen, PRP, Proth.exe
Decimal Digits:213723   (log10 is 213722.14108282)
Rank (*):25081 (digit rank is 1)
Entrance Rank (*):135
Currently on list? (*):no
Submitted:5/21/2005 19:08:47 CDT
Last modified:7/27/2005 08:20:02 CDT
Database id:74546
Status Flags:none
Score (*):41.8924 (normalized score 0.0768)

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 42.991111337946
Subcategory: "Divides GF(*,5)"
(archival tag id 187133, tag last modified 2020-10-29 19:20:16)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 32, weight 42.991111337946
Subcategory: "Divides GF(*,3)"
(archival tag id 187132, 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_id74546
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -f -t -q"3*2^709968+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3*2^709968+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 76628537 Running N-1 test using base 11 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) Reduced from FFT(98304,17) to FFT(98304,16) 1419948 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^709968+1 is prime! (10301.2767s+0.0006s)
modified2020-07-07 17:30:43
created2005-05-21 19:23:00
id79579

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