21562 · 3109 · 828814575031420 · 955637315837480 · 672198801383498 · 162946224587484 · 258724139309335 · 327170641169422 · 880151556857437 - 1
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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:21562 · 3109 · 828814575031420 · 955637315837480 · 672198801383498 · 162946224587484 · 258724139309335 · 327170641169422 · 880151556857437 - 1
Verification status (*):PRP
Official Comment:Sophie Germain (p)
Proof-code(s): (*):p360 : Kinne, Exoo, OpenPFGW
Decimal Digits:36498   (log10 is 36497.537925566)
Rank (*):55415 (digit rank is 4)
Entrance Rank (*):49207
Currently on list? (*):short
Submitted:12/14/2013 21:38:35 CDT
Last modified:12/17/2013 07:51:17 CDT
Database id:116639
Status Flags:Verify, TrialDiv
Score (*):36.4453 (normalized score 0.0006)

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.
Sophie Germain (p) (archivable *)
Prime on list: yes, rank 14
Subcategory: "Sophie Germain (p)"
(archival tag id 217525, tag last modified 2016-04-02 09:20:06)

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.
machineRedHat P4 P4
notesPFGW Version [GWNUM 26.5]
Primality testing 2^1562*3^109*828814575031^420*955637315837^480*672198801383^498*162946224587^484*258724139309^335*327170641169^422*880151556857^437-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Calling Brillhart-Lehmer-Selfridge with factored part 1.43%
2^1562*3^109*828814575031^420*955637315837^480*672198801383^498*162946224587^484*258724139309^335*327170641169^422*880151556857^437-1 is Lucas PRP! (391.6518s+0.0051s)
[Elapsed time: 6.53 minutes]
modified2013-12-14 21:59:33
created2013-12-14 21:53:01

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.