4267 · 2701052 + 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:4267 · 2701052 + 1
Verification status (*):Proven
Official Comment:Divides GF(701051,5)
Proof-code(s): (*):L1204 : Brown1, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:211042   (log10 is 211041.31064287)
Rank (*):21992 (digit rank is 1)
Entrance Rank (*):3123
Currently on list? (*):no
Submitted:9/3/2011 08:40:18 CDT
Last modified:9/3/2011 09:50:41 CDT
Database id:101650
Status Flags:none
Score (*):41.8536 (normalized score 0.1222)

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.
Generalized Fermat Divisors (bases 3,5,6,10,12) (archivable *)
Prime on list: no, rank 26, weight 50.2123331685311
Subcategory: "Divides GF(*,5)"
(archival tag id 213410, tag last modified 2016-03-15 13:57:15)

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_id101650
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 4267 2 701052 1 2>&1
[Elapsed time: 9.997 seconds]
modified2011-12-27 16:48:29
created2011-09-03 08:48:01
id132812

fieldvalue
prime_id101650
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"4267*2^701052+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 4267*2^701052+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
4267*2^701052+1 is prime! (1396.0868s+0.0006s)
[Elapsed time: 23.27 minutes]
modified2011-12-27 16:48:29
created2011-09-03 09:05:30
id132822

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.