6835 · 2458114 + 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:6835 · 2458114 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L687 : Slomma, Srsieve, PrimeGrid, LLR
Decimal Digits:137910   (log10 is 137909.89017213)
Rank (*):35846 (digit rank is 1)
Entrance Rank (*):3697
Currently on list? (*):no
Submitted:6/9/2009 11:58:33 CDT
Last modified:6/9/2009 12:50:20 CDT
Removed (*):10/8/2009 07:15:17 CDT
Database id:88788
Status Flags:none
Score (*):40.5442 (normalized score 0.0299)

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_id88788
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 6835 2 458114 1 2>&1
[Elapsed time: 9.452 seconds]
modified2011-12-27 16:48:43
created2009-06-09 12:05:01
id106942

fieldvalue
prime_id88788
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -t -q"6835*2^458114+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 6835*2^458114+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(57344,20) to FFT(57344,19)
Reduced from FFT(57344,19) to FFT(57344,18)
Reduced from FFT(57344,18) to FFT(57344,17)
Reduced from FFT(57344,17) to FFT(57344,16)
916262 bit request FFT size=(57344,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
6835*2^458114+1 is prime! (1101.4900s+0.0000s)
[Elapsed time: 18.48 minutes]
modified2009-07-10 15:55:51
created2009-06-09 12:14:12
id106944

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