57 · 22747499 + 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:57 · 22747499 + 1
Verification status (*):Proven
Official Comment:Divides Fermat F(2747497)
Proof-code(s): (*):L3514 : Bishop1, PSieve, Srsieve, PrimeGrid, OpenPFGW, LLR
Decimal Digits:827082   (log10 is 827081.36793165)
Rank (*):315 (digit rank is 1)
Entrance Rank (*):101
Currently on list? (*):short
Submitted:5/14/2013 10:07:48 CDT
Last modified:5/14/2013 17:50:04 CDT
Database id:114144
Status Flags:none
Score (*):46.0504 (normalized score 10.1935)

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.
Fermat Divisors (archivable *)
Prime on list: yes, rank 2, weight 50.093488512537
Subcategory: "Divides Fermat"
(archival tag id 217153, tag last modified 2016-03-15 13:57:14)

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_id114144
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"57*2^2747499+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 57*2^2747499+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
57*2^2747499+1 is prime! (15507.8831s+0.0018s)
[Elapsed time: 4.31 hours]
modified2013-06-04 07:30:39
created2013-05-14 10:08:01
id158665

fieldvalue
prime_id114144
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 57 2 2747499 1 2>&1
[Elapsed time: 10.640 seconds]
modified2013-06-04 07:30:39
created2013-05-14 10:18:02
id158666

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.