10362600 + 666 · 10181299 + 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:10362600 + 666 · 10181299 + 1
Verification status (*):Proven
Official Comment:Palindrome
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p363 : Batalov, OpenPFGW
Decimal Digits:362601   (log10 is 362600)
Rank (*):11372 (digit rank is 1)
Entrance Rank (*):4853
Currently on list? (*):short
Submitted:11/15/2014 00:31:34 CDT
Last modified:11/15/2014 03:20:21 CDT
Database id:118770
Status Flags:TrialDiv
Score (*):43.5179 (normalized score 0.606)

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.
Palindrome (archivable *)
Prime on list: yes, rank 3
Subcategory: "Palindrome"
(archival tag id 217853, tag last modified 2014-11-16 14:50:32)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Serge Batalov writes (15 Nov 2014): 
Inspired by the use of Belphegor's Prime in Episode "Just a Regular Irregular" of the "Elementary" TV series.

Extends the OEIS series A156166

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"10^362600+666*10^181299+1" 2>&1
PFGW Version [GWNUM 27.11]
Primality testing 10^362600+666*10^181299+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 11
Running N-1 test using base 13
Calling Brillhart-Lehmer-Selfridge with factored part 34.95%


10^362600+666*10^181299+1 is prime! (8322.2006s+0.0103s)
[Elapsed time: 2.31 hours]
modified2014-12-15 15:47:31
created2014-11-15 00:41:01

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.