211208 · 5121626 - 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:211208 · 5121626 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):p208 : Frase, Srsieve, SierpinskiRiesel, PRP, OpenPFGW
Decimal Digits:85019   (log10 is 85018.250457737)
Rank (*):45354 (digit rank is 1)
Entrance Rank (*):3960
Currently on list? (*):no
Submitted:10/27/2006 13:36:14 CDT
Last modified:10/27/2006 14:33:47 CDT
Removed (*):4/5/2007 05:06:00 CDT
Database id:78726
Status Flags:none
Score (*):39.0541 (normalized score 0.0071)

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_id78726
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 211208 5 121626 -1 2>&1
[Elapsed time: 8.860 seconds]
modified2007-03-03 21:00:43
created2006-10-27 13:52:01
id86550

fieldvalue
prime_id78726
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -tp -q"211208*5^121626-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 211208*5^121626-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
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)
564866 bit request FFT size=(32768,18)
Calling Brillhart-Lehmer-Selfridge with factored part 99.99%
211208*5^121626-1 is prime! (-1914.6873s+0.0200s)
[Elapsed time: 2446 seconds]
modified2007-03-03 21:00:43
created2006-10-27 13:53:01
id86551

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