3221449497221499 · 234567 + 5

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:3221449497221499 · 234567 + 5
Verification status (*):PRP
Official Comment (*):Triplet (3), ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c58 : Kaiser1, NewPGen, OpenPFGW, Primo
Decimal Digits:10422   (log10 is 10421.211911444)
Rank (*):77398 (digit rank is 1)
Entrance Rank (*):69135
Currently on list? (*):short
Submitted:8/31/2015 10:22:32 CDT
Last modified:8/31/2015 10:50:35 CDT
Database id:120299
Status Flags:Verify, TrialDiv
Score (*):32.568 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 199
Subcategory: "ECPP"
(archival tag id 218071, tag last modified 2021-09-18 09:37:41)
Triplet (archivable class *)
Prime on list: yes, rank 5
Subcategory: "Triplet (3)"
(archival tag id 218072, tag last modified 2021-06-05 07:37:30)

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.

Peter Kaiser writes (1 Sep 2015):  (report abuse)
Primo certificate: http://factordb.com/cert.php?id=1100000000802018844

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"3221449497221499*2^34567+5" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 3221449497221499*2^34567+5 [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% (0.41% proof) 3221449497221499*2^34567+5 is Fermat and Lucas PRP! (8.0366s+0.0065s) [Elapsed time: 8.00 seconds]
modified2020-07-07 17:30:17
created2015-08-31 10:40:22

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.
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