16 · (205743162092 · 2777# - 1) + 15

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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:	16 · (205743162092 · 2777# - 1) + 15
Verification status (*):	Proven
Official Comment (*):	Cunningham chain (16p+15)
Proof-code(s): (*):	p429 : Steinberg, MultiSieve, OpenPFGW
Decimal Digits:	1197 (log₁₀ is 1196.0725077081)
Rank (*):	117966 (digit rank is 41)
Entrance Rank (*):	115766
Currently on list? (*):	no
Submitted:	3/11/2023 16:47:49 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	135758
Status Flags:	none
Score (*):	25.8319 (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.

Cunningham Chains (1st kind) (archivable class *)
Prime on list: no, rank 7, weight 46.585657944444
Subcategory: "Cunningham chain (16p+15)"
(archival tag id 228347, tag last modified 2024-02-17 00:37:26)

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 135758

person_id 9

machine Using: Digital Ocean Droplet

what prime

notes Command: /var/www/clientpool/1/pfgw64 -tc -q"16*(205743162092*2777#-1)+15" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 16*(205743162092*2777#-1)+15 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2791
Running N+1 test using discriminant 2843, base 1+sqrt(2843)
Running N+1 test using discriminant 2843, base 2+sqrt(2843)
Calling N+1 BLS with factored part 100.00% and helper 0.03% (300.03% proof)

16*(205743162092*2777#-1)+15 is prime! (1.9313s+0.0004s)
[Elapsed time: 2.00 seconds]

modified 2023-03-11 17:31:36

created 2023-03-11 17:31:34

id 181533

field	value
prime_id	135758
person_id	9
machine	Using: Digital Ocean Droplet
what	prime
notes	Command: /var/www/clientpool/1/pfgw64 -tc -q"16(2057431620922777#-1)+15" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 16(2057431620922777#-1)+15 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2791 Running N+1 test using discriminant 2843, base 1+sqrt(2843) Running N+1 test using discriminant 2843, base 2+sqrt(2843) Calling N+1 BLS with factored part 100.00% and helper 0.03% (300.03% proof) 16(2057431620922777#-1)+15 is prime! (1.9313s+0.0004s) [Elapsed time: 2.00 seconds]
modified	2023-03-11 17:31:36
created	2023-03-11 17:31:34
id	181533

Query times: 0.0002 seconds to select prime, 0.0004 seconds to seek comments.