V(193201)

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:V(193201)
Verification status (*):PRP
Official Comment (*):Lucas number, ECPP
Proof-code(s): (*):E4 : Childers, CM
Decimal Digits:40377   (log10 is 40376.621083936)
Rank (*):65049 (digit rank is 2)
Entrance Rank (*):63134
Currently on list? (*):yes
Submitted:12/15/2023 23:03:36 UTC
Last modified:12/16/2023 03:37:29 UTC
Database id:136771
Status Flags:Verify
Score (*):36.7572 (normalized score 0.0002)

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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: yes, rank 14
Subcategory: "ECPP"
(archival tag id 229053, tag last modified 2024-10-27 10:37:10)
Lucas Number (archivable *)
Prime on list: yes, rank 2
Subcategory: "Lucas Number"
(archival tag id 229054, tag last modified 2023-12-16 03:37:32)

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_id136771
person_id9
machineUsing: Digital Ocean Droplet
whatprp
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tc -q"V(193201)" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing V(193201) [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial


Running N-1 test using base 17
Generic modular reduction using generic reduction AVX-512 FFT length 12800 on A 134129-bit number
Running N-1 test using base 19
Generic modular reduction using generic reduction AVX-512 FFT length 12800 on A 134129-bit number
Running N+1 test using discriminant 37, base 15+sqrt(37)
Generic modular reduction using generic reduction AVX-512 FFT length 12800 on A 134129-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 50/135310 ERROR: ROUND OFF 0.45905>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 37, base 15+sqrt(37)
Generic modular reduction using generic reduction AVX-512 FFT length 16K on A 134129-bit number
Calling N-1 BLS with factored part 0.90% and helper 0.21% (2.91% proof)


V(193201) is Fermat and Lucas PRP! (107.6656s+0.0092s)
[Elapsed time: 1.83 minutes]
modified2023-12-16 03:11:57
created2023-12-16 03:10:07
id182606

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