138281163736 · 6977# + 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:	138281163736 · 6977# + 1
Verification status (*):	Proven
Official Comment (*):	Cunningham chain 2nd kind (8p-7)
Proof-code(s): (*):	p395 : Angel, Augustin, NewPGen, OpenPFGW
Decimal Digits:	3006 (log₁₀ is 3005.1079355595)
Rank (*):	97238 (digit rank is 2)
Entrance Rank (*):	84007
Currently on list? (*):	yes
Submitted:	7/26/2016 14:17:36 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	121949
Status Flags:	none
Score (*):	28.7058 (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 (2nd kind) (archivable class *)
Prime on list: yes, rank 3, weight 44.678955287142
Subcategory: "Cunningham chain 2nd kind (8p-7)"
(archival tag id 218373, 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 121949

person_id 9

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

what prime

notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"138281163736*6977#+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 138281163736*6977#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 6991 Calling Brillhart-Lehmer-Selfridge with factored part 33.40% 138281163736*6977#+1 is prime! (0.6525s+0.0005s) [Elapsed time: 1.00 seconds]

modified 2020-07-07 22:30:16

created 2016-07-26 14:23:01

id 167588

field	value
prime_id	121949
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/clientpool/1/pfgw64 -t -q"1382811637366977#+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 1382811637366977#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 6991 Calling Brillhart-Lehmer-Selfridge with factored part 33.40% 138281163736*6977#+1 is prime! (0.6525s+0.0005s) [Elapsed time: 1.00 seconds]
modified	2020-07-07 22:30:16
created	2016-07-26 14:23:01
id	167588

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