339143232768 + 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:339143232768 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):p317 : Chambers, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:213988   (log10 is 213987.59386825)
Rank (*):24829 (digit rank is 1)
Entrance Rank (*):2023
Currently on list? (*):no
Submitted:1/19/2011 22:10:31 CDT
Last modified:2/13/2011 12:10:58 CDT
Removed (*):2/26/2012 11:24:08 CDT
Database id:97518
Status Flags:none
Score (*):41.8963 (normalized score 0.0794)

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 (archivable *)
Prime on list: no, rank 2039
Subcategory: "Generalized Fermat"
(archival tag id 213089, tag last modified 2021-09-20 18:37:22)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 3391432 32768 1 2>&1 [Elapsed time: 7.474 seconds]
modified2020-07-07 17:30:32
created2011-01-19 22:18:01

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"3391432^32768+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3391432^32768+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 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) 1421712 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 51.38% 3391432^32768+1 is prime! (-421.0646s+0.0400s) [Elapsed time: 2.56 hours]
modified2020-07-07 17:30:32
created2011-01-19 22:38:02

Query times: 0.0003 seconds to select prime, 0.0033 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.