3214654524288 + 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.

Description:3214654524288 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L4309 : Kecic, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR
Decimal Digits:3411613   (log10 is 3411612.39418935)
Rank (*):39 (digit rank is 1)
Entrance Rank (*):30
Currently on list? (*):short
Submitted:12/25/2019 06:02:28 CDT
Last modified:12/29/2019 11:50:20 CDT
Database id:130199
Status Flags:TrialDiv
Score (*):50.395 (normalized score 491.2704)

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.
Generalized Fermat (archivable *)
Prime on list: yes, rank 5
Subcategory: "Generalized Fermat"
(archival tag id 223655, tag last modified 2020-06-04 13:20:26)

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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 -t -q"3214654^524288+1" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 3214654^524288+1 [N-1, Brillhart-Lehmer-Selfridge] F: 3214654^524288+1 16384/36012170 (trial factor to 1442980243) F: 3214654^524288+1 34816/36012170 (trial factor to 1442980243) F: 3214654^524288+1 53248/36012170 (trial factor to 1442980243) Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 95.37% 3214654^524288+1 is prime! (364920.2327s+0.1426s) [Elapsed time: 4.22 days]
modified2020-07-07 17:30:10
created2019-12-25 06:11:02

Query times: 0.0009 seconds to select prime, 0.0002 seconds to seek comments.
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