195262026 · 24001# + 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:	195262026 · 24001# + 1
Verification status (*):	Proven
Official Comment (*):	Arithmetic progression (5,d=10601738*24001#)
Proof-code(s): (*):	p155 : DavisK, NewPGen, OpenPFGW
Decimal Digits:	10377 (log₁₀ is 10376.818348678)
Rank (*):	83573 (digit rank is 7)
Entrance Rank (*):	73374
Currently on list? (*):	yes
Submitted:	7/19/2018 04:28:45 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	125477
Status Flags:	none
Score (*):	32.5547 (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 48.004841896371
Subcategory: "5/5"
(archival tag id 230285, tag last modified 2025-01-18 22:37:22)

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 125477

person_id 9

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

what prime

notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"195262026*24001#+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 195262026*24001#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 24007 Calling Brillhart-Lehmer-Selfridge with factored part 33.36% 195262026*24001#+1 is prime! (14.0402s+0.0026s) [Elapsed time: 14.00 seconds]

modified 2020-07-07 22:30:14

created 2018-07-19 04:33:50

id 171150

field	value
prime_id	125477
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/clientpool/1/pfgw64 -t -q"19526202624001#+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 19526202624001#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 24007 Calling Brillhart-Lehmer-Selfridge with factored part 33.36% 195262026*24001#+1 is prime! (14.0402s+0.0026s) [Elapsed time: 14.00 seconds]
modified	2020-07-07 22:30:14
created	2018-07-19 04:33:50
id	171150

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.