9 · 10212903 - 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:9 · 10212903 - 1
Verification status (*):Proven
Official Comment:Near-repdigit
Proof-code(s): (*):p297 : Broadhurst, Srsieve, NewPGen, LLR, OpenPFGW
Decimal Digits:212904   (log10 is 212903.95424251)
Rank (*):22299 (digit rank is 1)
Entrance Rank (*):1753
Currently on list? (*):no
Submitted:11/4/2010 15:32:38 CDT
Last modified:11/21/2010 16:02:22 CDT
Database id:95898
Status Flags:none
Score (*):41.8807 (normalized score 0.1156)

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 57
Subcategory: "Near-repdigit"
(archival tag id 211045, tag last modified 2019-04-14 05:20:23)

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.
fieldvalue
prime_id95898
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/pfgw -o -f -q"10^212904-10^212903-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
10^212904-10^212903-1 1/1


trial factoring to 76316188
10^212904-10^212903-1 has no small factor.
[Elapsed time: 1169.902 seconds]
modified2011-12-27 16:48:36
created2010-11-04 15:54:18
id121185

fieldvalue
prime_id95898
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tp -q"10^212904-10^212903-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 10^212904-10^212903-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling Brillhart-Lehmer-Selfridge with factored part 69.90%
10^212904-10^212903-1 is prime! (-350.1138s+0.0600s)
[Elapsed time: 7.15 hours]
modified2010-11-28 11:14:55
created2010-11-04 15:53:01
id121184

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