9985628193 · 2171009 + 1
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
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 (*):52482 (digit rank is 1)
Entrance Rank (*):49228
Currently on list? (*):short
Submitted:7/12/2016 03:14:48 CDT
Last modified:7/12/2016 03:50:39 CDT
Database id:121892
Status Flags:TrialDiv
Score (*):37.5076 (normalized score 0.0015)

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 37.2297320443746
Subcategory: "Cunningham chain 2nd kind (2p-1)"
(archival tag id 218363, tag last modified 2017-12-20 01:20:25)

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 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"9985628193*2^171009+1" 2>&1
PFGW Version [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]
modified2017-01-27 05:57:11
created2016-07-12 03:21:01

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.