250216 · 5460797 - 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:250216 · 5460797 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):p284 : Fredriksen, Srsieve, SierpinskiRiesel, OpenPFGW
Decimal Digits:322089   (log10 is 322088.6794031)
Rank (*):14277 (digit rank is 1)
Entrance Rank (*):323
Currently on list? (*):no
Submitted:9/7/2010 07:03:59 CDT
Last modified:9/8/2010 01:20:23 CDT
Removed (*):12/4/2013 19:35:43 CDT
Database id:94532
Status Flags:none
Score (*):43.1537 (normalized score 0.3763)

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_id94532
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 250216 5 460797 -1 2>&1
[Elapsed time: 9.836 seconds]
modified2011-12-27 16:48:38
created2010-09-07 07:05:02
id118446

fieldvalue
prime_id94532
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -tp -q"250216*5^460797-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 250216*5^460797-1 [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(131072,20) to FFT(131072,19)
Reduced from FFT(131072,19) to FFT(131072,18)
Reduced from FFT(131072,18) to FFT(131072,17)
2139928 bit request FFT size=(131072,17)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
250216*5^460797-1 is prime! (-1130.2694s+0.0700s)
[Elapsed time: 17.92 hours]
modified2010-10-13 12:41:35
created2010-09-07 07:08:01
id118447

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.