2316765173284 · 3593# + 16061
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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:2316765173284 · 3593# + 16061
Verification status (*):PRP
Official Comment:Quintuplet (1), ECPP
Proof-code(s): (*):c18 : Luhn, Primo
Decimal Digits:1543   (log10 is 1542.7749052196)
Rank (*):101125 (digit rank is 5)
Entrance Rank (*):93765
Currently on list? (*):short
Submitted:10/15/2016 14:33:15 CDT
Last modified:10/15/2016 19:20:03 CDT
Database id:122380
Status Flags:Verify, TrialDiv
Score (*):26.6272 (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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 838
Subcategory: "ECPP"
(archival tag id 218469, tag last modified 2019-06-02 14:20:07)
Quintuplet (archivable class *)
Prime on list: yes, rank 2
Subcategory: "Quintuplet (1)"
(archival tag id 218470, tag last modified 2017-11-30 12:50:21)

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tc -q"2316765173284*3593#+16061" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing 2316765173284*3593#+16061 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 7, base 2+sqrt(7)
Calling N-1 BLS with factored part 0.92% and helper 0.25% (3.06% proof)

2316765173284*3593#+16061 is Fermat and Lucas PRP! (0.4351s+0.0006s)
[Elapsed time: 0.00 seconds]
modified2017-01-27 05:57:10
created2016-10-15 14:42:53

Query times: 0.001 seconds to select prime, 0.0007 seconds to seek comments.