2782511886988 · 2347# - 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:	2782511886988 · 2347# - 1
Verification status (*):	Proven
Official Comment (*):	Cunningham chain (2p+1)
Proof-code(s): (*):	p364 : Batalov, NewPGen, OpenPFGW
Decimal Digits:	1006 (log₁₀ is 1005.0760759566)
Rank (*):	131887 (digit rank is 1294)
Entrance Rank (*):	112238
Currently on list? (*):	no
Submitted:	7/20/2014 02:46:37 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	118228
Status Flags:	none
Score (*):	25.2878 (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 89, weight 25.00996518267
Subcategory: "Cunningham chain (2p+1)"
(archival tag id 217764, 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 118228

person_id 9

machine Xeon 4c+4c 3.5GHz

what prime

notes Command: /home/caldwell/client/pfgw/pfgw64 -tp -q"2782511886988*2347#-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 2782511886988*2347#-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 2357, base 1+sqrt(2357) Calling Brillhart-Lehmer-Selfridge with factored part 33.64% 2782511886988*2347#-1 is prime! (0.1752s+0.0001s) [Elapsed time: 0.00 seconds]

modified 2020-07-07 22:30:17

created 2014-07-20 02:51:19

id 163794

field	value
prime_id	118228
person_id	9
machine	Xeon 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/client/pfgw/pfgw64 -tp -q"27825118869882347#-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 27825118869882347#-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 2357, base 1+sqrt(2357) Calling Brillhart-Lehmer-Selfridge with factored part 33.64% 2782511886988*2347#-1 is prime! (0.1752s+0.0001s) [Elapsed time: 0.00 seconds]
modified	2020-07-07 22:30:17
created	2014-07-20 02:51:19
id	163794

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