98166!/3 - 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:	98166!/3 - 1
Verification status (*):	Proven
Official Comment (*):	[none]
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	p381 : Batalov, Fpsieve, OpenPFGW
Decimal Digits:	447411 (log₁₀ is 447410.31869332)
Rank (*):	11749 (digit rank is 1)
Entrance Rank (*):	1593
Currently on list? (*):	no
Submitted:	2/22/2015 01:38:47 UTC
Last modified:	5/20/2023 20:59:19 UTC
Removed (*):	3/24/2020 02:37:49 UTC
Database id:	119403
Status Flags:	none
Score (*):	44.1637 (normalized score 0.4398)

User comments about this prime (disclaimer):

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Serge Batalov writes (24 Feb 2015): (report abuse)

There are at least 36 OEIS sequences for "near-factorial" numbers (in addition to factorial plus one A002981 and minus one A002982):
Numbers such that m*n!-1 is a prime (2<=m<=10): A076133, A076134, A099350, A099351, A180627-A180631.
Numbers such that m*n!+1 is a prime: A051915, A076679-A076683, A178488, A180626, A126896.
Numbers such that n!/m-1 is a prime: A082671, A139056, A139199-A139205.
Numbers such that n!/m+1 is a prime: A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071.

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 119403

person_id 9

machine Using: Xeon 4c+4c 3.5GHz

what prime

notes Command: /home/caldwell/client/pfgw/pfgw64 -tp -q"98166!/3-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 98166!/3-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 98179, base 1+sqrt(98179) Calling Brillhart-Lehmer-Selfridge with factored part 33.41% 98166!/3-1 is prime! (19572.7278s+0.2011s) [Elapsed time: 5.44 hours]

modified 2020-07-07 22:30:17

created 2015-02-22 01:43:01

id 165009

field	value
prime_id	119403
person_id	9
machine	Using: Xeon 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/client/pfgw/pfgw64 -tp -q"98166!/3-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 98166!/3-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 98179, base 1+sqrt(98179) Calling Brillhart-Lehmer-Selfridge with factored part 33.41% 98166!/3-1 is prime! (19572.7278s+0.2011s) [Elapsed time: 5.44 hours]
modified	2020-07-07 22:30:17
created	2015-02-22 01:43:01
id	165009

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