U(106663)/35892566541651557

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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:	U(106663)/35892566541651557
Verification status (*):	PRP
Official Comment (*):	Fibonacci cofactor, ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	E1 : Batalov, CM
Decimal Digits:	22275 (log₁₀ is 22274.344182467)
Rank (*):	72666 (digit rank is 1)
Entrance Rank (*):	72512
Currently on list? (*):	short
Submitted:	3/30/2024 06:03:54 UTC
Last modified:	3/30/2024 06:37:13 UTC
Database id:	137898
Status Flags:	Verify
Score (*):	34.9193 (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 71
Subcategory: "ECPP"
(archival tag id 229468, tag last modified 2024-04-24 05:37:25)
Fibonacci cofactor (archivable *)
Prime on list: yes, rank 3
Subcategory: "Fibonacci cofactor"
(archival tag id 229469, tag last modified 2024-04-19 02:37:11)

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 (30 Mar 2024): (report abuse)

Certificate is at FactorDB.com

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 137898

person_id 9

machine Using: Digital Ocean Droplet

what prp

notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"U(106663)/35892566541651557" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing U(106663)/35892566541651557 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 3
Generic modular reduction using generic reduction AVX-512 FFT length 7K on A 73994-bit number
Running N+1 test using discriminant 11, base 11+sqrt(11)
Generic modular reduction using generic reduction AVX-512 FFT length 7K on A 73994-bit number
Calling N-1 BLS with factored part 0.06% and helper 0.05% (0.24% proof)

U(106663)/35892566541651557 is Fermat and Lucas PRP! (20.9949s+0.0074s)
[Elapsed time: 25.00 seconds]

modified 2024-03-30 06:04:27

created 2024-03-30 06:04:02

id 183740

field	value
prime_id	137898
person_id	9
machine	Using: Digital Ocean Droplet
what	prp
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -tc -q"U(106663)/35892566541651557" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing U(106663)/35892566541651557 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 3 Generic modular reduction using generic reduction AVX-512 FFT length 7K on A 73994-bit number Running N+1 test using discriminant 11, base 11+sqrt(11) Generic modular reduction using generic reduction AVX-512 FFT length 7K on A 73994-bit number Calling N-1 BLS with factored part 0.06% and helper 0.05% (0.24% proof) U(106663)/35892566541651557 is Fermat and Lucas PRP! (20.9949s+0.0074s) [Elapsed time: 25.00 seconds]
modified	2024-03-30 06:04:27
created	2024-03-30 06:04:02
id	183740

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.