35425016208 · 2399# + 1

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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:	35425016208 · 2399# + 1
Verification status (*):	Proven
Official Comment (*):	Arithmetic progression (8,d=176389517*2399#)
Proof-code(s): (*):	p41 : Luhn, OpenPFGW
Decimal Digits:	1034 (log₁₀ is 1033.5665944673)
Rank (*):	128711 (digit rank is 37)
Entrance Rank (*):	128674
Currently on list? (*):	no
Submitted:	2/21/2025 05:46:27 UTC
Last modified:	2/21/2025 11:37:27 UTC
Database id:	139968
Status Flags:	none
Score (*):	25.3753 (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.

Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 8, weight 48.025004149261
Subcategory: "8/8"
(archival tag id 238976, tag last modified 2025-02-21 11:37:36)

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 139968

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"35425016208*2399#+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 35425016208*2399#+1 [N-1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 2411
Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3434-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.59%

35425016208*2399#+1 is prime! (0.0985s+0.0004s)
[Elapsed time: 5.00 seconds]

modified 2025-02-21 11:04:50

created 2025-02-21 11:04:45

id 186061

field	value
prime_id	139968
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"354250162082399#+1" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 354250162082399#+1 [N-1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 2411 Generic modular reduction using generic reduction FMA3 FFT length 320 on A 3434-bit number Calling Brillhart-Lehmer-Selfridge with factored part 33.59% 35425016208*2399#+1 is prime! (0.0985s+0.0004s) [Elapsed time: 5.00 seconds]
modified	2025-02-21 11:04:50
created	2025-02-21 11:04:45
id	186061

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