2316765173284 · 3593# + 16061

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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:	2316765173284 · 3593# + 16061
Verification status (*):	PRP
Official Comment (*):	Quintuplet (1), ECPP
Proof-code(s): (*):	c18 : Luhn, Primo
Decimal Digits:	1543 (log₁₀ is 1542.7749052196)
Rank (*):	109886 (digit rank is 5)
Entrance Rank (*):	93765
Currently on list? (*):	yes
Submitted:	10/15/2016 19:33:15 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	122380
Status Flags:	Verify
Score (*):	26.6272 (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.

Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 1026
Subcategory: "ECPP"
(archival tag id 218469, tag last modified 2024-12-16 19:37:11)
Quintuplet (archivable class *)
Prime on list: yes, rank 5
Subcategory: "Quintuplet (1)"
(archival tag id 218470, 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 122380

person_id 9

machine Using: Xeon 4c+4c 3.5GHz

what prp

notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"2316765173284*3593#+16061" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 2316765173284*3593#+16061 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N-1 BLS with factored part 0.92% and helper 0.25% (3.06% proof) 2316765173284*3593#+16061 is Fermat and Lucas PRP! (0.4351s+0.0006s) [Elapsed time: 0.00 seconds]

modified 2020-07-07 22:30:16

created 2016-10-15 19:42:53

id 168025

field	value
prime_id	122380
person_id	9
machine	Using: Xeon 4c+4c 3.5GHz
what	prp
notes	Command: /home/caldwell/client/pfgw/pfgw64 -tc -q"23167651732843593#+16061" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 23167651732843593#+16061 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N-1 BLS with factored part 0.92% and helper 0.25% (3.06% proof) 2316765173284*3593#+16061 is Fermat and Lucas PRP! (0.4351s+0.0006s) [Elapsed time: 0.00 seconds]
modified	2020-07-07 22:30:16
created	2016-10-15 19:42:53
id	168025

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