449209457832 · 3307# + 1633050403

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:449209457832 · 3307# + 1633050403
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (5,d=30), ECPP
Proof-code(s): (*):c98 : Batalov, EMsieve, Primo
Decimal Digits:1408   (log10 is 1407.6123170763)
Rank (*):110771 (digit rank is 4)
Entrance Rank (*):105446
Currently on list? (*):short
Submitted:10/12/2021 04:03:11 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:132822
Status Flags:Verify
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: yes, rank 3
Subcategory: "Consecutive primes in arithmetic progression (5,d=*)"
(archival tag id 226354, tag last modified 2023-03-11 15:53:59)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 685, weight 38.794443592238
Subcategory: "Arithmetic progression (5,d=*)"
(archival tag id 226355, tag last modified 2023-03-11 15:53:59)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 1030
Subcategory: "ECPP"
(archival tag id 226356, tag last modified 2024-06-24 15:37:19)

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#+1633050403" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 449209457832*3307#+1633050403 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 5, base 1+sqrt(5) Calling N+1 BLS with factored part 0.88% and helper 0.04% (2.72% proof) 449209457832*3307#+1633050403 is Fermat and Lucas PRP! (0.1095s+0.0003s) [Elapsed time: 0.00 seconds]
modified2022-07-11 18:21:46
created2021-10-12 04:06:03

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