288465! + 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:	288465! + 1
Verification status (*):	Proven
Official Comment (*):	Factorial
Proof-code(s): (*):	p3 : Dohmen, OpenPFGW
Decimal Digits:	1449771 (log₁₀ is 1449770.1352724)
Rank (*):	518 (digit rank is 1)
Entrance Rank (*):	292
Currently on list? (*):	short
Submitted:	1/10/2022 16:08:16 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	133139
Status Flags:	none
Score (*):	47.7722 (normalized score 16.2468)

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.

Factorial primes (archivable *)
Prime on list: yes, rank 3
Subcategory: "Factorial"
(archival tag id 226622, tag last modified 2023-03-11 15:53:59)

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 133139

person_id 9

machine Using: Xeon (pool) 4c+4c 3.5GHz

what prime

notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"288465!+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 288465!+1 [N-1, Brillhart-Lehmer-Selfridge] F: 288465!+1 2048/15274792 (trial factor to 584346506) Running N-1 test using base 288467 Running N-1 test using base 288481 Calling Brillhart-Lehmer-Selfridge with factored part 33.75% 288465!+1 is prime! (155936.6640s+2.3692s) [Elapsed time: 1.80 days]

modified 2022-07-11 18:21:45

created 2022-01-10 16:11:01

id 178852

field	value
prime_id	133139
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/clientpool/1/pfgw64 -t -q"288465!+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 288465!+1 [N-1, Brillhart-Lehmer-Selfridge] F: 288465!+1 2048/15274792 (trial factor to 584346506) Running N-1 test using base 288467 Running N-1 test using base 288481 Calling Brillhart-Lehmer-Selfridge with factored part 33.75% 288465!+1 is prime! (155936.6640s+2.3692s) [Elapsed time: 1.80 days]
modified	2022-07-11 18:21:45
created	2022-01-10 16:11:01
id	178852

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