10290253 - 2 · 10145126 - 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:10290253 - 2 · 10145126 - 1
Verification status (*):Proven
Official Comment:Near-repdigit, Palindrome
Proof-code(s): (*):p235 : Bedwell, OpenPFGW
Decimal Digits:290253   (log10 is 290253)
Rank (*):15806 (digit rank is 1)
Entrance Rank (*):1873
Currently on list? (*):short
Submitted:4/11/2012 05:07:30 CDT
Last modified:4/11/2012 17:50:24 CDT
Database id:106219
Status Flags:none
Score (*):42.8338 (normalized score 0.2957)

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.
Near-repdigit (archivable *)
Prime on list: no, rank 37
Subcategory: "Near-repdigit"
(archival tag id 214299, tag last modified 2019-04-14 05:20:23)
Palindrome (archivable *)
Prime on list: yes, rank 7
Subcategory: "Palindrome"
(archival tag id 214300, tag last modified 2014-11-16 14:50:32)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -tp -q"10^290253-2*10^145126-1" 2>&1
PFGW Version [GWNUM 26.5]
Primality testing 10^290253-2*10^145126-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 34.95%
10^290253-2*10^145126-1 is prime! (44136.7571s+0.0184s)
[Elapsed time: 12.26 hours]
modified2012-07-16 11:33:01
created2012-04-11 05:08:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -o -f -q"10^290253-2*10^145126-1" 2>&1
PFGW Version [GWNUM 26.5]
10^290253-2*10^145126-1 1/1 mro=0

trial factoring to 106133972
10^290253-2*10^145126-1 has no small factor.
[Elapsed time: 2587.869 seconds]
modified2012-07-16 11:33:01
created2012-04-11 05:18:01

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.