556336461 · 2211356 + 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.

This prime's information:

Description:556336461 · 2211356 + 1
Verification status (*):Proven
Official Comment (*):Cunningham chain 2nd kind (2p-1)
Proof-code(s): (*):L3494 : Batalov, NewPGen, LLR
Decimal Digits:63634   (log10 is 63633.24110108)
Rank (*):53274 (digit rank is 1)
Entrance Rank (*):48468
Currently on list? (*):short
Submitted:5/24/2019 10:32:56 CDT
Last modified:5/25/2019 06:50:03 CDT
Database id:126495
Status Flags:TrialDiv
Score (*):38.1608 (normalized score 0.0014)

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: yes, rank 5, weight 37.88300874981
Subcategory: "Cunningham chain 2nd kind (2p-1)"
(archival tag id 220272, tag last modified 2020-06-02 14:12:08)

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 (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -t -q"556336461*2^211356+1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 556336461*2^211356+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 99.99% 556336461*2^211356+1 is prime! (21.9533s+0.0003s) [Elapsed time: 22.00 seconds]
modified2020-07-07 17:30:13
created2019-05-24 10:33:26

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.