4 · 31499606 + 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:4 · 31499606 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Proof-code(s): (*):L4962 : Baur, Srsieve, NewPGen, LLR
Decimal Digits:715495   (log10 is 715494.49836513)
Rank (*):2557 (digit rank is 1)
Entrance Rank (*):1266
Currently on list? (*):yes
Submitted:1/16/2020 04:55:58 CDT
Last modified:1/16/2020 06:50:20 CDT
Database id:130259
Status Flags:TrialDiv
Score (*):45.6055 (normalized score 2.7519)

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 668
Subcategory: "Generalized Fermat"
(archival tag id 223675, tag last modified 2022-06-27 21:37:10)

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"4*3^1499606+1" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 4*3^1499606+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 5 Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 2376820/2376822 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N-1 test using base 11 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 4*3^1499606+1 is prime! (5502.2716s+0.0083s) [Elapsed time: 1.53 hours]
modified2020-07-07 17:30:10
created2020-01-16 05:01:01

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.