2683143625525 · 235176 + 13

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:2683143625525 · 235176 + 13
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (3,d=6),ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c92 : Lamprecht, Luhn, Primo
Decimal Digits:10602   (log10 is 10601.459771397)
Rank (*):75496 (digit rank is 2)
Entrance Rank (*):74668
Currently on list? (*):short
Submitted:12/30/2019 22:23:49 CDT
Last modified:12/30/2019 22:50:24 CDT
Database id:130217
Status Flags:Verify, TrialDiv
Score (*):32.6211 (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.
Consecutive Primes in Arithmetic Progression (archivable class *)
Prime on list: yes, rank 3
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 223656, tag last modified 2020-04-27 12:20:26)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 127, weight 38.2267473221382
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 223657, tag last modified 2020-04-27 12:20:25)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 162
Subcategory: "ECPP"
(archival tag id 223658, tag last modified 2020-06-22 13:50:28)

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.

Norman Luhn writes (30 Dec 2019):  (report abuse)

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"2683143625525*2^35176+13" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 2683143625525*2^35176+13 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 4+sqrt(5) Calling N-1 BLS with factored part 0.14% and helper 0.01% (0.43% proof) 2683143625525*2^35176+13 is Fermat and Lucas PRP! (2.7766s+0.0001s) [Elapsed time: 3.00 seconds]
modified2020-07-07 17:30:10
created2019-12-30 22:31:05

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