2968802755 · 2459# + 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:2968802755 · 2459# + 1
Verification status (*):Proven
Official Comment:Arithmetic progression (8,d=359463429*2459#)
Proof-code(s): (*):p155 : DavisK, NewPGen, OpenPFGW
Decimal Digits:1057   (log10 is 1056.1935088357)
Rank (*):117693 (digit rank is 48)
Entrance Rank (*):78841
Currently on list? (*):short
Submitted:4/20/2009 21:52:36 CDT
Last modified:4/20/2009 22:25:13 CDT
Database id:87789
Status Flags:none
Score (*):25.443 (normalized score 0)

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.
Arithmetic Progressions of Primes (archivable class *)
Prime on list: yes, rank 3, weight 48.1577209595356
Subcategory: "Arithmetic progression (8,d=*)"
(archival tag id 208979, tag last modified 2019-08-11 02:50:12)

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 2968802755 2459 # 1 2>&1
[Elapsed time: 150.101 seconds]
modified2011-12-27 16:48:44
created2009-04-20 22:22:42

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"2968802755*2459#+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 2968802755*2459#+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(448,22) to FFT(448,21)
Reduced from FFT(448,21) to FFT(448,20)
Reduced from FFT(448,20) to FFT(448,19)
Reduced from FFT(448,19) to FFT(448,18)
Reduced from FFT(448,18) to FFT(448,17)
Reduced from FFT(448,17) to FFT(448,16)
7026 bit request FFT size=(448,16)
Calling Brillhart-Lehmer-Selfridge with factored part 33.44%
2968802755*2459#+1 is prime! (3.0866s+0.0005s)
[Elapsed time: 3.00 seconds]
modified2009-05-25 07:25:56
created2009-04-20 22:08:42

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