214916 · 31934246 - 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:214916 · 31934246 - 1
Verification status (*):Proven
Official Comment (*):Generalized Woodall
Proof-code(s): (*):L4965 : Propper, LLR
Decimal Digits:922876   (log10 is 922875.21072524)
Rank (*):3095 (digit rank is 1)
Entrance Rank (*):2427
Currently on list? (*):short
Submitted:4/21/2023 19:07:16 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:135972
Status Flags:none
Score (*):46.3867 (normalized score 3.9338)

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 Woodall (archivable *)
Prime on list: yes, rank 16
Subcategory: "Generalized Woodall"
(archival tag id 228508, tag last modified 2024-02-26 15:37:18)

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.
fieldvalue
prime_id135972
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -tp -q"214916*3^1934246-1" 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 214916*3^1934246-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using AVX-512 FFT length 300K, Pass1=960, Pass2=320, clm=1 on 214916*3^1934246-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 95/3065726 ERROR: ROUND OFF 0.45774>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using AVX-512 FFT length 320K, Pass1=128, Pass2=2560, clm=2 on 214916*3^1934246-1
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 1177763/3065726 ERROR: ROUND OFF 0.45536>0.45
(Test aborted, try again using the -a2 (or possibly -a0) switch)
Running N+1 test using discriminant 5, base 1+sqrt(5)
Special modular reduction using AVX-512 FFT length 336K, Pass1=896, Pass2=384, clm=1 on 214916*3^1934246-1
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%


214916*3^1934246-1 is prime! (31253.6203s+0.0182s)
[Elapsed time: 8.68 hours]
modified2023-04-22 03:48:55
created2023-04-21 19:08:01
id181786

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