270694 · 5123231 - 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:270694 · 5123231 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):p213 : Zahn, Srsieve, SierpinskiRiesel, PRP, OpenPFGW
Decimal Digits:86141   (log10 is 86140.205082961)
Rank (*):45227 (digit rank is 1)
Entrance Rank (*):3871
Currently on list? (*):no
Submitted:10/28/2006 11:16:36 CDT
Last modified:10/28/2006 12:05:22 CDT
Removed (*):4/15/2007 18:51:53 CDT
Database id:78737
Status Flags:none
Score (*):39.0945 (normalized score 0.0074)

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_id78737
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 270694 5 123231 -1 2>&1
[Elapsed time: 9.138 seconds]
modified2007-03-03 21:00:43
created2006-10-28 11:22:02
id86572

fieldvalue
prime_id78737
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tp -q"270694*5^123231-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 270694*5^123231-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 11, base 1+sqrt(11)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(32768,20) to FFT(32768,19)
Reduced from FFT(32768,19) to FFT(32768,18)
572320 bit request FFT size=(32768,18)
Calling Brillhart-Lehmer-Selfridge with factored part 99.99%
270694*5^123231-1 is prime! (-1844.8373s+0.0100s)
[Elapsed time: 2541 seconds]
modified2007-03-03 21:00:43
created2006-10-28 11:23:01
id86573

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