2683143625525 · 235176 + 1

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:2683143625525 · 235176 + 1
Verification status (*):Proven
Official Comment (*):Consecutive primes arithmetic progression (1,d=6)
Proof-code(s): (*):p407 : Lamprecht, Luhn, OpenPFGW
Decimal Digits:10602   (log10 is 10601.459771397)
Rank (*):82138 (digit rank is 4)
Entrance Rank (*):74668
Currently on list? (*):short
Submitted:12/31/2019 04:21:34 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:130215
Status Flags:none
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 4
Subcategory: "Consecutive primes in arithmetic progression (1,d=*)"
(archival tag id 223662, tag last modified 2023-03-11 15:53:59)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 117
Subcategory: "Arithmetic progression (1,d=*)"
(archival tag id 223663, 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.
fieldvalue
prime_id130215
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/4/pfgw64 -t -q"2683143625525*2^35176+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 2683143625525*2^35176+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 99.88% 2683143625525*2^35176+1 is prime! (0.8455s+0.0002s) [Elapsed time: 1.00 seconds]
modified2020-07-07 22:30:10
created2019-12-31 04:23:02
id175901

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