222361 · 22854840 + 1
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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:222361 · 22854840 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):g403 : Yoshimura, ProthSieve, PrimeSierpinski, LLR, Proth.exe
Decimal Digits:859398   (log10 is 859397.81987998)
Rank (*):468 (digit rank is 1)
Entrance Rank (*):14
Currently on list? (*):short
Submitted:9/5/2006 03:19:46 CDT
Last modified:9/6/2006 00:09:25 CDT
Database id:78430
Status Flags:none
Score (*):46.168 (normalized score 10.6156)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 222361 2 2854840 1 2>&1
[Elapsed time: 10.655 seconds]
modified2007-03-03 21:00:43
created2006-09-05 03:22:01

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"222361*2^2854840+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 222361*2^2854840+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(393216,19) to FFT(393216,18)
Reduced from FFT(393216,18) to FFT(393216,17)
Reduced from FFT(393216,17) to FFT(393216,16)
5709724 bit request FFT size=(393216,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
222361*2^2854840+1 is prime! (-275.2840s+0.0000s)
[Elapsed time: 74783 seconds]
modified2007-03-03 21:00:43
created2006-09-05 03:23:02

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.