(282939 - 1)/883323903012540278033571819073

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:(282939 - 1)/883323903012540278033571819073
Verification status (*):PRP
Official Comment (*):Mersenne cofactor, ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c84 : Underwood, Primo
Decimal Digits:24938   (log10 is 24937.180690392)
Rank (*):66185 (digit rank is 1)
Entrance Rank (*):65697
Currently on list? (*):short
Submitted:2/24/2021 00:28:32 CDT
Last modified:2/24/2021 00:50:25 CDT
Database id:132049
Status Flags:Verify, TrialDiv
Score (*):35.2685 (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 18
Subcategory: "ECPP"
(archival tag id 226023, tag last modified 2021-05-04 10:20:37)
Mersenne cofactor (archivable *)
Prime on list: yes, rank 2
Subcategory: "Mersenne cofactor"
(archival tag id 226024, tag last modified 2021-02-24 00:50:28)

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.

Paul Underwood writes (2 Mar 2021):  (report abuse)
Certificate available at factorDB or ellipsa.eu

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_id132049
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"(2^82939-1)/883323903012540278033571819073" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing (2^82939-1)/8833239030...3571819073 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N-1 BLS with factored part 0.06% and helper 0.02% (0.19% proof) (2^82939-1)/8833239030...3571819073 is Fermat and Lucas PRP! (53.3501s+0.0002s) [Elapsed time: 54.00 seconds]
modified2021-04-20 17:39:24
created2021-02-24 00:31:01
id177748

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