(284211 - 1)/1347377 / 31358793176711980763958121 / 3314641676042347824169591561

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.

Description:(284211 - 1)/1347377 / 31358793176711980763958121 / 3314641676042347824169591561
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c95 : Gelhar, Primo
Decimal Digits:25291   (log10 is 25290.890679803)
Rank (*):64959 (digit rank is 1)
Entrance Rank (*):64824
Currently on list? (*):short
Submitted:9/27/2020 14:32:23 CDT
Last modified:9/27/2020 14:50:23 CDT
Database id:131278
Status Flags:Verify, TrialDiv
Score (*):35.312 (normalized score 0.0001)

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: yes, rank 11
Subcategory: "ECPP"
(archival tag id 225672, tag last modified 2020-09-27 14:50:25)
Mersenne cofactor (archivable *)
Prime on list: yes, rank 1
Subcategory: "Mersenne cofactor"
(archival tag id 225673, tag last modified 2020-09-27 14:50:27)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Robert Gelhar writes (27 Sep 2020):  (report abuse)
Certificate can be found listed on https://www.ellipsa.eu/public/primo/top20.html

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.
fieldvalue
prime_id131278
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"(2^84211-1)/1347377/31358793176711980763958121/3314641676042347824169591561" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing (2^84211-1)/1347377/3135879317...0763958121/3314641676...4169591561 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N-1 test using base 11
Running N+1 test using discriminant 19, base 1+sqrt(19)
Calling N+1 BLS with factored part 0.05% and helper 0.05% (0.22% proof)


(2^84211-1)/1347377/3135879317...0763958121/3314641676...4169591561 is Fermat and Lucas PRP! (53.3037s+0.0004s)
[Elapsed time: 53.00 seconds]
modified2020-09-27 14:36:54
created2020-09-27 14:36:01
id176966

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
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