35701614404 · 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:	35701614404 · 2399# + 1
Verification status (*):	Proven
Official Comment (*):	Arithmetic progression (3,d=50135224*2399#)
Proof-code(s): (*):	p41 : Luhn, OpenPFGW
Decimal Digits:	1034 (log₁₀ is 1033.5699722648)
Rank (*):	128707 (digit rank is 33)
Entrance Rank (*):	128511
Currently on list? (*):	yes
Submitted:	2/16/2025 06:53:45 UTC
Last modified:	2/17/2025 06:37:29 UTC
Database id:	139803
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: yes, rank 5, weight 29.816920155081
Subcategory: "3/8"
(archival tag id 238913, tag last modified 2025-02-17 06:37:36)

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 139803

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"35701614404*2399#+1" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 35701614404*2399#+1 [N-1, Brillhart-Lehmer-Selfridge]
trial

Running N-1 test using base 2417
Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3434-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 33.47%

35701614404*2399#+1 is prime! (0.2768s+0.0002s)
[Elapsed time: 5.00 seconds]

modified 2025-02-17 06:23:55

created 2025-02-17 06:23:50

id 185896

field	value
prime_id	139803
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -V -f -t -q"357016144042399#+1" >command_output 2>&1 PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11] Primality testing 357016144042399#+1 [N-1, Brillhart-Lehmer-Selfridge] trial Running N-1 test using base 2417 Generic modular reduction using generic reduction AVX-512 FFT length 1K on A 3434-bit number Calling Brillhart-Lehmer-Selfridge with factored part 33.47% 35701614404*2399#+1 is prime! (0.2768s+0.0002s) [Elapsed time: 5.00 seconds]
modified	2025-02-17 06:23:55
created	2025-02-17 06:23:50
id	185896

Query times: 0.0004 seconds to select prime, 0.001 seconds to seek comments.