2003663613 · 2195000 + 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:2003663613 · 2195000 + 1
Verification status (*):Proven
Official Comment:Twin (p+2)
Proof-code(s): (*):L202 : Vautier, McKibbon, Gribenko, NewPGen, PrimeGrid, TPS, LLR
Decimal Digits:58711   (log10 is 58710.150979288)
Rank (*):50107 (digit rank is 2)
Entrance Rank (*):9069
Currently on list? (*):short
Submitted:1/18/2007 10:06:58 CDT
Last modified:1/18/2007 13:50:03 CDT
Database id:79211
Status Flags:none
Score (*):37.9125 (normalized score 0.0022)

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.
Twin Primes (archivable *)
Prime on list: yes, rank 8
Subcategory: "Twin (p+2)"
(archival tag id 188988, tag last modified 2017-07-04 19:20:06)

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 2003663613 2 195000 1 2>&1
[Elapsed time: 9.573 seconds]
modified2007-03-03 21:00:42
created2007-01-18 10:22:40

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"2003663613*2^195000+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2003663613*2^195000+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(24576,20) to FFT(24576,19)
Reduced from FFT(24576,19) to FFT(24576,18)
Reduced from FFT(24576,18) to FFT(24576,17)
Reduced from FFT(24576,17) to FFT(24576,16)
390070 bit request FFT size=(24576,16)
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
2003663613*2^195000+1 is prime! (166.8800s+0.0000s)
[Elapsed time: 170 seconds]
modified2007-03-03 21:00:42
created2007-01-18 11:25:13

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