3 · 2303093 + 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 · 2303093 + 1
Verification status (*):Proven
Official Comment (*):Divides Fermat F(303088); GF(303088,3), GF(303086,6), GF(303092,10), GF(303088,12), GF(303092,5) [g0]
Proof-code(s): (*):Y : Young
Decimal Digits:91241   (log10 is 91240.561597038)
Rank (*):52506 (digit rank is 1)
Entrance Rank (*):7
Currently on list? (*):no
Submitted:2/1/1998 05:59:59 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:223
Status Flags:none
Score (*):39.2718 (normalized score 0.0033)

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 46, weight 40.370431577342
Subcategory: "Divides GF(*,5)"
(archival tag id 188453, tag last modified 2024-03-22 08:37:11)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 42, weight 40.370431577342
Subcategory: "Divides GF(*,12)"
(archival tag id 188452, tag last modified 2024-04-07 12:37:28)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 37, weight 40.370431577342
Subcategory: "Divides GF(*,10)"
(archival tag id 188451, tag last modified 2023-07-02 21:37:20)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 41, weight 40.370431577342
Subcategory: "Divides GF(*,6)"
(archival tag id 188450, tag last modified 2023-03-31 01:37:05)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 47, weight 40.370431577342
Subcategory: "Divides GF(*,3)"
(archival tag id 188449, tag last modified 2024-03-22 08:37:11)
Fermat Divisors (archivable *)
Prime on list: no, rank 32, weight 40.370431577342
Subcategory: "Divides Fermat"
(archival tag id 188448, tag last modified 2023-07-28 18:37:27)

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_id223
person_id9
machineWinXP P4 1.8GHz
whatprime
notesPFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N-1 test using base 5 Primality testing 3*2^303093+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3*2^303093+1 is prime! (798.688000 seconds)
modified2003-03-25 17:21:47
created2003-01-22 22:03:19
id67307

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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