13 · 2114296 + 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:13 · 2114296 + 1
Verification status (*):Proven
Official Comment (*):Divides Fermat F(114293); GF(114292,5), GF(114293,10) [g0]
Proof-code(s): (*):Y : Young
Decimal Digits:34408   (log10 is 34407.638327763)
Rank (*):66044 (digit rank is 1)
Entrance Rank (*):6
Currently on list? (*):no
Submitted:9/1/1995 04:59:59 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:2855
Status Flags:none
Score (*):36.2632 (normalized score 0.0001)

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 45, weight 38.828185407035
Subcategory: "Divides GF(*,10)"
(archival tag id 190798, tag last modified 2023-07-02 21:37:20)
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 54, weight 38.828185407035
Subcategory: "Divides GF(*,5)"
(archival tag id 190797, tag last modified 2024-03-22 08:37:11)
Fermat Divisors (archivable *)
Prime on list: no, rank 41, weight 38.828185407035
Subcategory: "Divides Fermat"
(archival tag id 190796, 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_id2855
person_id9
machineWinXP Athlon 1.3GHz
whatprime
notesPFGW Version 20021217.Win_Dev (Beta 'caveat utilitor') [FFT v22.7 w/P4] Running N-1 test using base 3 Primality testing 13*2^114296+1 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 13*2^114296+1 is prime! (147.011000 seconds)
modified2003-03-25 17:22:41
created2003-01-09 03:37:14
id64742

Query times: 0.0004 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.