9836347216384 + 1
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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:9836347216384 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Proof-code(s): (*):g398 : Yama, Yamada, Proth.exe
Decimal Digits:130955   (log10 is 130954.589797)
Rank (*):34828 (digit rank is 1)
Entrance Rank (*):2289
Currently on list? (*):no
Submitted:9/11/2008 17:18:56 CDT
Last modified:9/11/2008 18:19:16 CDT
Removed (*):7/24/2009 08:12:23 CDT
Database id:85505
Status Flags:none
Score (*):40.3849 (normalized score 0.0342)

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 695
Subcategory: "Generalized Fermat"
(archival tag id 204833, tag last modified 2017-12-09 07:20:23)

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_id85505
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 98363472 16384 1 2>&1
[Elapsed time: 7.223 seconds]
modified2011-12-27 16:48:46
created2008-09-11 17:22:02
id100477

fieldvalue
prime_id85505
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"98363472^16384+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 98363472^16384+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(57344,20) to FFT(57344,19)
Reduced from FFT(57344,19) to FFT(57344,18)
Reduced from FFT(57344,18) to FFT(57344,17)
Reduced from FFT(57344,17) to FFT(57344,16)
870052 bit request FFT size=(57344,16)
Calling Brillhart-Lehmer-Selfridge with factored part 50.43%
98363472^16384+1 is prime! (-1889.5973s+0.0200s)
[Elapsed time: 41.22 minutes]
modified2008-09-12 14:12:35
created2008-09-11 17:38:03
id100478

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.