2738129459017 · 4211# + 3399421637

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:2738129459017 · 4211# + 3399421637
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (5,d=30)
Proof-code(s): (*):c98 : Batalov, EMsieve, Primo
Decimal Digits:1805   (log10 is 1804.9340485097)
Rank (*):104184 (digit rank is 1)
Entrance Rank (*):103338
Currently on list? (*):short
Submitted:1/31/2022 12:49:13 CDT
Last modified:1/31/2022 13:37:09 CDT
Database id:133271
Status Flags:Verify, TrialDiv
Score (*):27.117 (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 1
Subcategory: "Consecutive primes in arithmetic progression (5,d=*)"
(archival tag id 226718, tag last modified 2022-01-31 13:37:11)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 681, weight 39.943568290283
Subcategory: "Arithmetic progression (5,d=*)"
(archival tag id 226719, tag last modified 2022-06-09 19:37:16)

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_id133271
person_id9
machineUsing: Dual Intel Xeon Gold 5222 CPUs 3.8GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"2738129459017*4211#+3399421637" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 2738129459017*4211#+3399421637 [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 17, base 1+sqrt(17)
Calling N-1 BLS with factored part 0.50% and helper 0.18% (1.72% proof)


2738129459017*4211#+3399421637 is Fermat and Lucas PRP! (0.1385s+0.0001s)
[Elapsed time: 0.00 seconds]
modified2022-01-31 12:51:02
created2022-01-31 12:51:02
id178993

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.