49 · 21646042 + 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:49 · 21646042 + 1
Verification status (*):Proven
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L2516 : Koschewski, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:495510   (log10 is 495509.70631881)
Rank (*):4858 (digit rank is 1)
Entrance Rank (*):153
Currently on list? (*):yes
Submitted:7/31/2011 00:08:49 CDT
Last modified:7/31/2011 08:20:03 CDT
Database id:100949
Status Flags:none
Score (*):44.4774 (normalized score 1.0182)

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 1603
Subcategory: "Generalized Fermat"
(archival tag id 213338, tag last modified 2021-12-07 23:37:18)

User comments about this prime (disclaimer):

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Marc Koschewski writes (11 Sep 2014):  (report abuse)
Divides xGF(1646041,5,4)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 49 2 1646042 1 2>&1 [Elapsed time: 10.071 seconds]
modified2020-07-07 17:30:31
created2011-07-31 00:18:33

machineRedHat Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"49*2^1646042+1" 2>&1 PFGW Version [GWNUM 25.14] Primality testing 49*2^1646042+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 49*2^1646042+1 is prime! (2908.5259s+0.0300s) [Elapsed time: 48.57 minutes]
modified2020-07-07 17:30:31
created2011-07-31 00:20:45

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