3933508262144 + 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:3933508262144 + 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:1728783   (log10 is 1728782.01822318)
Rank (*):138 (digit rank is 1)
Entrance Rank (*):57
Currently on list? (*):short
Submitted:1/27/2018 21:34:14 CDT
Last modified:1/28/2018 18:20:19 CDT
Database id:124190
Status Flags:TrialDiv
Score (*):48.3119 (normalized score 59.4953)

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: no, rank 35
Subcategory: "Generalized Fermat"
(archival tag id 218986, tag last modified 2020-08-28 06:20:21)

User comments about this prime (disclaimer):

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PrimeGrid writes (30 Jan 2018):  (report abuse)
For more details, please see the official announcement.

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"3933508^262144+1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 3933508^262144+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 90.87% 3933508^262144+1 is prime! (73257.6076s+0.0584s) [Elapsed time: 20.35 hours]
modified2020-07-07 17:30:15
created2018-01-27 21:41:01

Query times: 0.0005 seconds to select prime, 0.0009 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.