9985628193 · 2171009 + 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:9985628193 · 2171009 + 1
Verification status (*):Proven
Official Comment (*):Cunningham chain 2nd kind (2p-1)
Proof-code(s): (*):L109 : Nair, NewPGen, LLR
Decimal Digits:51489   (log10 is 51488.837903893)
Rank (*):60559 (digit rank is 1)
Entrance Rank (*):49228
Currently on list? (*):no
Submitted:7/12/2016 08:14:48 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:121892
Status Flags:none
Score (*):37.5076 (normalized score 0.0005)

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 10, weight 37.229732044375
Subcategory: "Cunningham chain 2nd kind (2p-1)"
(archival tag id 218363, tag last modified 2023-11-26 09:37:12)

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_id121892
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"9985628193*2^171009+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 9985628193*2^171009+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 99.98% 9985628193*2^171009+1 is prime! (18.8392s+0.0003s) [Elapsed time: 19.00 seconds]
modified2020-07-07 22:30:16
created2016-07-12 08:21:01
id167530

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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