V(116593)/120790349

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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(116593)/120790349
Verification status (*):	PRP
Official Comment (*):	Lucas cofactor, ECPP
Proof-code(s): (*):	E4 : Childers, CM
Decimal Digits:	24359 (log₁₀ is 24358.41390743)
Rank (*):	72238 (digit rank is 1)
Entrance Rank (*):	70180
Currently on list? (*):	yes
Submitted:	11/9/2023 02:44:11 UTC
Last modified:	11/9/2023 03:37:12 UTC
Database id:	136631
Status Flags:	Verify
Score (*):	35.1959 (normalized score 0)

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: no, rank 68
Subcategory: "ECPP"
(archival tag id 228936, tag last modified 2024-10-27 10:37:10)
Lucas cofactor (archivable *)
Prime on list: yes, rank 4
Subcategory: "Lucas cofactor"
(archival tag id 228937, tag last modified 2024-04-24 05:37:27)

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.

field value

prime_id 136631

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"V(116593)/120790349" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing V(116593)/120790349 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 2
Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 80917-bit number
Running N+1 test using discriminant 23, base 1+sqrt(23)
Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 80917-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 44/80929 ERROR: ROUND OFF 0.49931>0.45
(Test aborted, try again using the -a1 switch)
Running N+1 test using discriminant 23, base 1+sqrt(23)
Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 80917-bit number
Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate
Iteration: 63689/80929 ERROR: ROUND OFF 0.5>0.45
(Test aborted, try again using the -a2 (or possibly -a0) switch)
Running N+1 test using discriminant 23, base 1+sqrt(23)
Generic modular reduction using generic reduction AVX-512 FFT length 9K on A 80917-bit number
Calling N-1 BLS with factored part 0.07% and helper 0.01% (0.22% proof)

V(116593)/120790349 is Fermat and Lucas PRP! (50.3534s+0.0135s)
[Elapsed time: 55.00 seconds]

modified 2023-11-09 02:45:56

created 2023-11-09 02:45:01

id 182466

field	value
prime_id	136631
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"V(116593)/120790349" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing V(116593)/120790349 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 2 Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 80917-bit number Running N+1 test using discriminant 23, base 1+sqrt(23) Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 80917-bit number Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 44/80929 ERROR: ROUND OFF 0.49931>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 23, base 1+sqrt(23) Generic modular reduction using generic reduction AVX-512 FFT length 8K, Pass1=128, Pass2=64, clm=1 on A 80917-bit number Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 63689/80929 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a2 (or possibly -a0) switch) Running N+1 test using discriminant 23, base 1+sqrt(23) Generic modular reduction using generic reduction AVX-512 FFT length 9K on A 80917-bit number Calling N-1 BLS with factored part 0.07% and helper 0.01% (0.22% proof) V(116593)/120790349 is Fermat and Lucas PRP! (50.3534s+0.0135s) [Elapsed time: 55.00 seconds]
modified	2023-11-09 02:45:56
created	2023-11-09 02:45:01
id	182466

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