(2850713831 - 1)/28506

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:(2850713831 - 1)/28506
Verification status (*):PRP
Official Comment (*):Generalized repunit
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):CH12 : Propper, Batalov, OpenPFGW, Primo, CHG
Decimal Digits:61612   (log10 is 61611.979477796)
Rank (*):53084 (digit rank is 1)
Entrance Rank (*):50143
Currently on list? (*):short
Submitted:8/21/2020 15:45:37 CDT
Last modified:4/21/2021 13:25:38 CDT
Database id:131079
Status Flags:Verify, TrialDiv
Score (*):38.0613 (normalized score 0.0014)

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.
Generalized Repunit (archivable *)
Prime on list: yes, rank 9
Subcategory: "Generalized Repunit"
(archival tag id 225643, tag last modified 2020-11-08 16:50:07)

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.

Serge Batalov writes (21 Aug 2020):  (report abuse)
CHG proof at 26.982% N-1 factorization is available at dropbox.
This proof relies on an ECPP certificate of a 16312-digit helper prime that divide N-1.

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_id131079
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/4/pfgw64 -tc -q"(28507^13831-1)/28506" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing (28507^13831-1)/28506 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 5 Running N+1 test using discriminant 37, base 12+sqrt(37) Calling N-1 BLS with factored part 0.14% and helper 0.00% (0.42% proof) (28507^13831-1)/28506 is Fermat and Lucas PRP! (354.2318s+0.0015s) [Elapsed time: 5.90 minutes]
modified2021-04-20 17:39:26
created2020-08-21 15:46:01
id176767

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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