75898524288 + 1
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The nth Prime Page will now find any of the first 2,623,557,157,654,233 primes or π(x) for x up to 100,000,000,000,000,000.

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:75898524288 + 1
Verification status (*):External
Official Comment:Generalized Fermat
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):p334 : Goetz, GeneferCUDA, AthGFNSieve, PrimeGrid, OpenPFGW
Decimal Digits:2558647   (log10 is 2558646.20024324)
Rank (*):23 (digit rank is 1)
Entrance Rank (*):13
Currently on list? (*):short
Submitted:11/19/2011 21:17:58 CDT
Last modified:11/19/2011 21:20:48 CDT
Database id:103235
Status Flags:none
Score (*):49.5136 (normalized score 325.3664)

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: yes, rank 4
Subcategory: "Generalized Fermat"
(archival tag id 213648, tag last modified 2012-08-14 21:20:05)

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.

PrimeGrid writes (11 Sep 2014): 
For more information, please see the Official Announcement.

Chris Caldwell writes (11 Sep 2014): 
Primality testing 75898^524288+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 50.05%
75898^524288+1 is prime! (667567.0963s+0.1473s)

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_id103235
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 75898 524288 1 2>&1
[Elapsed time: 8.886 seconds]
modified2011-12-27 16:48:26
created2011-11-19 21:18:01
id136054

Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.