449209457832 · 3307# + 1633050373

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:449209457832 · 3307# + 1633050373
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (4,d=30), ECPP
Proof-code(s): (*):c98 : Batalov, EMsieve, Primo
Decimal Digits:1408   (log10 is 1407.6123170763)
Rank (*):105485 (digit rank is 5)
Entrance Rank (*):105446
Currently on list? (*):no
Submitted:10/11/2021 23:03:11 CDT
Last modified:10/11/2021 23:37:22 CDT
Database id:132821
Status Flags:Verify, TrialDiv
Score (*):26.3408 (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: no, rank 15
Subcategory: "Consecutive primes in arithmetic progression (4,d=*)"
(archival tag id 226357, tag last modified 2021-10-14 15:37:18)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 736, weight 34.795353145975
Subcategory: "Arithmetic progression (4,d=*)"
(archival tag id 226358, tag last modified 2021-10-14 15:37:18)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 901
Subcategory: "ECPP"
(archival tag id 226359, tag last modified 2021-10-14 15:37:18)

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"449209457832*3307#+1633050373" 2>&1
PFGW Version [GWNUM 29.8]
Primality testing 449209457832*3307#+1633050373 [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 13, base 8+sqrt(13)
Calling N+1 BLS with factored part 0.15% and helper 0.06% (0.56% proof)

449209457832*3307#+1633050373 is Fermat and Lucas PRP! (0.1333s+0.0002s)
[Elapsed time: 0.00 seconds]
modified2021-10-11 23:06:03
created2021-10-11 23:06:03

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.