2570606397 · 2252763 + 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:2570606397 · 2252763 + 1
Verification status (*):Proven
Official Comment (*):Cunningham chain 2nd kind (2p-1)
Proof-code(s): (*):p364 : Batalov, NewPGen, OpenPFGW
Decimal Digits:76099   (log10 is 76098.654829599)
Rank (*):47934 (digit rank is 1)
Entrance Rank (*):47516
Currently on list? (*):short
Submitted:5/20/2020 19:05:47 CDT
Last modified:5/20/2020 19:20:16 CDT
Database id:130912
Status Flags:TrialDiv
Score (*):38.7124 (normalized score 0.0039)

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 2, weight 38.4346201387456
Subcategory: "Cunningham chain 2nd kind (2p-1)"
(archival tag id 224016, tag last modified 2020-06-02 11:16:40)

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.
fieldvalue
prime_id130912
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"2570606397*2^252763+1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 2570606397*2^252763+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 99.99% 2570606397*2^252763+1 is prime! (30.1861s+0.0003s) [Elapsed time: 30.00 seconds]
modified2020-07-07 17:30:10
created2020-05-20 19:06:01
id176598

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.