9850333616384 + 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:9850333616384 + 1
Verification status (*):Proven
Official Comment:Generalized Fermat
Proof-code(s): (*):g419 : Nilsson_R, AthGFNSieve, GFNSearch, GFN16Sieve, Proth.exe
Decimal Digits:130965   (log10 is 130964.70018364)
Rank (*):36778 (digit rank is 2)
Entrance Rank (*):4020
Currently on list? (*):no
Submitted:5/13/2009 02:10:50 CDT
Last modified:5/23/2009 08:08:00 CDT
Removed (*):7/24/2009 16:39:11 CDT
Database id:88236
Status Flags:none
Score (*):40.3851 (normalized score 0.0255)

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 1211
Subcategory: "Generalized Fermat"
(archival tag id 210448, tag last modified 2019-10-14 07:50:12)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1 98503336 16384 1 2>&1
[Elapsed time: 7.136 seconds]
modified2011-12-27 16:48:44
created2009-05-13 02:18:30

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"98503336^16384+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 98503336^16384+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
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)
870120 bit request FFT size=(57344,16)
Calling Brillhart-Lehmer-Selfridge with factored part 88.70%
98503336^16384+1 is prime! (-1710.1373s+0.0300s)
[Elapsed time: 43.78 minutes]
modified2009-05-25 07:25:55
created2009-05-13 02:38:01

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.