3481 · 21084608 + 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:3481 · 21084608 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L3452 : Resto, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:326504   (log10 is 326503.08324114)
Rank (*):16030 (digit rank is 1)
Entrance Rank (*):2327
Currently on list? (*):no
Submitted:3/21/2013 06:49:49 CDT
Last modified:3/21/2013 09:20:27 CDT
Removed (*):1/10/2014 14:15:20 CDT
Database id:111727
Status Flags:none
Score (*):43.1956 (normalized score 0.2914)

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 1953
Subcategory: "Generalized Fermat"
(archival tag id 215206, tag last modified 2021-09-18 19:37:18)

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 3481 2 1084608 1 2>&1 [Elapsed time: 10.005 seconds]
modified2020-07-07 17:30:22
created2013-03-21 06:52:24

machineWinXP Dual Core 2.6GHz Laptop
notesCommand: pfgw64.exe -t -q"3481*2^1084608+1" 2>&1 PFGW Version [GWNUM 27.8] Primality testing 3481*2^1084608+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3481*2^1084608+1 is prime! (543.0947s+0.0040s) [Elapsed time: 544 seconds]
modified2020-07-07 17:30:22
created2013-03-21 09:07:09

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.