485 · 2338297 + 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:485 · 2338297 + 1
Verification status (*):Proven
Official Comment:Divides Fermat F(338295) [K]
Proof-code(s): (*):L203 : Murata, LLR
Decimal Digits:101841   (log10 is 101840.23018488)
Rank (*):40207 (digit rank is 1)
Entrance Rank (*):3062
Currently on list? (*):no
Submitted:5/8/2007 06:40:22 CDT
Last modified:8/22/2007 23:20:23 CDT
Database id:80389
Status Flags:none
Score (*):39.6104 (normalized score 0.0124)

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: no, rank 26, weight 45.7946132116173
Subcategory: "Divides Fermat"
(archival tag id 188039, 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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 485 2 338297 1 2>&1
[Elapsed time: 9.158 seconds]
modified2007-05-30 21:58:14
created2007-05-08 06:52:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"485*2^338297+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 485*2^338297+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(49152,20) to FFT(49152,19)
Reduced from FFT(49152,19) to FFT(49152,18)
Reduced from FFT(49152,18) to FFT(49152,17)
Reduced from FFT(49152,17) to FFT(49152,16)
676620 bit request FFT size=(49152,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
485*2^338297+1 is prime! (708.1800s+0.0000s)
[Elapsed time: 713 seconds]
modified2007-05-30 21:58:14
created2007-05-08 06:53:01

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