457829032768 + 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:457829032768 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Proof-code(s): (*):p343 : Brown1, GeneFer, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:218258   (log10 is 218257.92568447)
Rank (*):21164 (digit rank is 1)
Entrance Rank (*):4395
Currently on list? (*):no
Submitted:2/20/2012 11:19:45 CDT
Last modified:2/20/2012 13:20:22 CDT
Removed (*):3/16/2012 05:26:20 CDT
Database id:104848
Status Flags:none
Score (*):41.9571 (normalized score 0.1361)

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 (archivable *)
Prime on list: no, rank 851
Subcategory: "Generalized Fermat"
(archival tag id 214056, tag last modified 2019-02-16 20:50:13)

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_id104848
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"4578290^32768+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 4578290^32768+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 84.99%
4578290^32768+1 is prime! (5413.9740s+0.0130s)
[Elapsed time: 1.50 hours]
modified2012-07-16 11:33:02
created2012-02-20 11:23:01
id139286

fieldvalue
prime_id104848
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 1 4578290 32768 1 2>&1
[Elapsed time: 7.639 seconds]
modified2012-07-16 11:33:02
created2012-02-20 11:35:01
id139287

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