primV(143234)

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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:	primV(143234)
Verification status (*):	PRP
Official Comment (*):	Lucas primitive part, ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	E1 : Batalov, CM
Decimal Digits:	23654 (log₁₀ is 23653.997928691)
Rank (*):	73026 (digit rank is 1)
Entrance Rank (*):	72919
Currently on list? (*):	yes
Submitted:	10/6/2024 20:28:56 UTC
Last modified:	10/7/2024 05:37:18 UTC
Database id:	138622
Status Flags:	Verify
Score (*):	35.1052 (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.

Lucas primitive part (archivable *)
Prime on list: yes, rank 5
Subcategory: "Lucas primitive part"
(archival tag id 229681, tag last modified 2024-10-11 22:37:11)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 76
Subcategory: "ECPP"
(archival tag id 229682, tag last modified 2024-10-27 10:37:10)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Serge Batalov writes (7 Oct 2024): (report abuse)

Certificate at FactorDB.

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 138622

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 9952419890...3292365121 [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 7680 on A 78577-bit number
Running N-1 test using base 19
Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 78577-bit number
Running N-1 test using base 37
Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 78577-bit number
Running N+1 test using discriminant 43, base 3+sqrt(43)
Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 78577-bit number
Calling N-1 BLS with factored part 0.25% and helper 0.01% (0.77% proof)

9952419890...3292365121 is Fermat and Lucas PRP! (36.5437s+0.0057s)
[Elapsed time: 40.00 seconds]

modified 2024-10-07 04:38:19

created 2024-10-07 04:37:33

id 184466

field	value
prime_id	138622
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 9952419890...3292365121 [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 7680 on A 78577-bit number Running N-1 test using base 19 Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 78577-bit number Running N-1 test using base 37 Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 78577-bit number Running N+1 test using discriminant 43, base 3+sqrt(43) Generic modular reduction using generic reduction AVX-512 FFT length 7680 on A 78577-bit number Calling N-1 BLS with factored part 0.25% and helper 0.01% (0.77% proof) 9952419890...3292365121 is Fermat and Lucas PRP! (36.5437s+0.0057s) [Elapsed time: 40.00 seconds]
modified	2024-10-07 04:38:19
created	2024-10-07 04:37:33
id	184466

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