74382396 · 23431# - 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:	74382396 · 23431# - 1
Verification status (*):	Proven
Official Comment (*):	Arithmetic progression (5,d=8829881*23431#)
Proof-code(s): (*):	p398 : Stocker, OpenPFGW
Decimal Digits:	10114 (log₁₀ is 10113.882596288)
Rank (*):	83342 (digit rank is 1)
Entrance Rank (*):	72489
Currently on list? (*):	no
Submitted:	7/12/2017 08:22:37 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	123739
Status Flags:	none
Score (*):	32.4752 (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 47.886798897394
Subcategory: "Arithmetic progression (5,d=*)"
(archival tag id 218846, 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 123739

person_id 9

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

what prime

notes Command: /home/caldwell/clientpool/1/pfgw64 -tp -q"74382396*23431#-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 74382396*23431#-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 23473, base 1+sqrt(23473) Calling Brillhart-Lehmer-Selfridge with factored part 33.34% 74382396*23431#-1 is prime! (33.0425s+0.0026s) [Elapsed time: 33.00 seconds]

modified 2020-07-07 22:30:15

created 2017-07-12 08:25:14

id 169392

field	value
prime_id	123739
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/clientpool/1/pfgw64 -tp -q"7438239623431#-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 7438239623431#-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 23473, base 1+sqrt(23473) Calling Brillhart-Lehmer-Selfridge with factored part 33.34% 74382396*23431#-1 is prime! (33.0425s+0.0026s) [Elapsed time: 33.00 seconds]
modified	2020-07-07 22:30:15
created	2017-07-12 08:25:14
id	169392

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