418059269664 · 2371# + 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:418059269664 · 2371# + 1
Verification status (*):Proven
Official Comment (*):Cunningham chain 2nd kind (16p-15)
Proof-code(s): (*):p308 : DavisK, Underwood, NewPGen, PrimeForm_egroup, OpenPFGW
Decimal Digits:1015   (log10 is 1014.3714205514)
Rank (*):122112 (digit rank is 33)
Entrance Rank (*):92253
Currently on list? (*):no
Submitted:4/17/2011 20:24:00 CDT
Last modified:4/17/2011 20:50:22 CDT
Database id:99745
Status Flags:none
Score (*):25.3166 (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.
Cunningham Chains (2nd kind) (archivable class *)
Prime on list: no, rank 11, weight 45.575990997424
Subcategory: "Cunningham chain 2nd kind (16p-15)"
(archival tag id 213207, tag last modified 2017-07-01 10:20:21)

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 Virtual STEM Server
notesCommand: /home/caldwell/client/pfgw -t -q"418059269664*2371#+1" 2>&1 PFGW Version [GWNUM 25.14] Primality testing 418059269664*2371#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2377 Calling Brillhart-Lehmer-Selfridge with factored part 33.45% 418059269664*2371#+1 is prime! (0.1474s+0.0002s) [Elapsed time: 1.00 seconds]
modified2020-07-07 17:30:31
created2011-04-17 20:25:24

machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 418059269664 2371 # 1 2>&1 [Elapsed time: 143.394 seconds]
modified2020-07-07 17:30:31
created2011-04-17 20:44:36

Query times: 0.0005 seconds to select prime, 0.0008 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.