308084! + 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:	308084! + 1
Verification status (*):	Proven
Official Comment (*):	Factorial
Proof-code(s): (*):	p425 : Propper, MultiSieve, OpenPFGW
Decimal Digits:	1557176 (log₁₀ is 1557175.1069149)
Rank (*):	546 (digit rank is 1)
Entrance Rank (*):	267
Currently on list? (*):	yes
Submitted:	1/20/2022 16:20:02 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	133196
Status Flags:	none
Score (*):	47.9914 (normalized score 17.5343)

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 2
Subcategory: "Factorial"
(archival tag id 226695, 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 133196

person_id 9

machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz

what prime

notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"308084!+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 308084!+1 [N-1, Brillhart-Lehmer-Selfridge] F: 308084!+1 2048/16409190 (trial factor to 630225089) Running N-1 test using base 308093 Running N-1 test using base 308101 Running N-1 test using base 308117 Calling Brillhart-Lehmer-Selfridge with factored part 33.56% 308084!+1 is prime! (142619.5473s+1.8969s) [Elapsed time: 1.65 days]

modified 2022-07-11 18:21:45

created 2022-01-20 16:31:01

id 178917

field	value
prime_id	133196
person_id	9
machine	Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
what	prime
notes	Command: /home/caldwell/clientpool/1/pfgw64 -t -q"308084!+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 308084!+1 [N-1, Brillhart-Lehmer-Selfridge] F: 308084!+1 2048/16409190 (trial factor to 630225089) Running N-1 test using base 308093 Running N-1 test using base 308101 Running N-1 test using base 308117 Calling Brillhart-Lehmer-Selfridge with factored part 33.56% 308084!+1 is prime! (142619.5473s+1.8969s) [Elapsed time: 1.65 days]
modified	2022-07-11 18:21:45
created	2022-01-20 16:31:01
id	178917

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