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Old 2010-12-31, 21:40   #1
ATH
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Default Happy Prime Year MMXI!

Still about 1h20min until new year here in Denmark, but I'm posting before the fireworks.

2011 is a prime year!

22011-1 has 2 factors: http://www.mersenne.org/report_expon...&B1=Get+status

2011 = 72+212+392 = 92+292+332 = 92+92+432 = 212+272+292

2011 = 28+33+123

3 natural disasters "predicted" for 2011 in various fiction:
http://www.virtuescience.com/2011.html

Other real world upcoming events:
http://en.wikipedia.org/wiki/2011
http://www.imdb.com/year/2011/
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Old 2010-12-31, 22:57   #2
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Quote:
Originally Posted by ATH View Post
2 known* factors.
http://factordb.com/index.php?query=M2011
The cofactor is a 558 digit composite number. Not too likely to be fully factored for quite a while.
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Old 2011-01-01, 05:59   #3
petrw1
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Default 1 minutes to go here.....

count down with me....
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Old 2011-01-01, 07:36   #4
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Quote:
Originally Posted by petrw1 View Post
count down with me....
-359,-360,-361....
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Old 2011-01-01, 08:04   #5
ixfd64
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Unfortunately, 2010 was a dry year, in the context of new Mersenne primes. Let's hope that 0b11111011011 will really be a "prime" year!
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Old 2011-01-01, 08:28   #6
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Quote:
Originally Posted by Mini-Geek View Post
The cofactor is a 558 digit composite number. Not too likely to be fully factored for quite a while.
What test is most commonly used to prove such a number composite?
FLT?
David
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Old 2011-01-01, 09:21   #7
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Quote:
Originally Posted by petrw1 View Post
count down with me....
-65980, -65981, -65982, ...

Also the 2011th prime is 17483.
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Old 2011-01-01, 12:29   #8
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Quote:
Originally Posted by davieddy View Post
What test is most commonly used to prove such a number composite?
FLT?
David
I'm not sure exactly what math is behind it, and it can probably vary depending on the program used to find the other factor, but some sort of PRP test is (AFAIK) most commonly used to show whether a cofactor in factoring (including Mersennes) is PRP or composite. A PRP test of such a small number is quite easy. PARI/GP can do it (with ispseudoprime; I think it would see that it's a base 2 Rabin-Miller PRP, then see that it's not a Lucas PRP) in ~50 ms on my computer.

Last fiddled with by Mini-Geek on 2011-01-01 at 12:41
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Old 2011-01-01, 16:05   #9
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Quote:
Originally Posted by Mini-Geek View Post
A PRP test of such a small number is quite easy. PARI/GP can do it (with ispseudoprime; I think it would see that it's a base 2 Rabin-Miller PRP, then see that it's not a Lucas PRP) in ~50 ms on my computer.
To test my understanding, this means it is a "pseudoprime"?

David

PS Does PRP = "Probably Prime"?
If so, what does the R stand for - "robably"?

Last fiddled with by davieddy on 2011-01-01 at 16:12
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Old 2011-01-01, 16:35   #10
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[QUOTE=davieddy;244241]PS Does PRP = "Probably Prime"?

It means "probable prime", which is a technical term meaning a number which passes one of certain designated tests.

It does not mean "probably prime". 1105 is a probable prime to many bases. (It's a Carmichael number.) But it's not probably prime. It's definitely composite.
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Old 2011-01-01, 16:39   #11
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Default To raise another chestnut (from the dead?)

...from either 10 or 11 years ago,

Happy 202nd decade to y'all

David

Last fiddled with by davieddy on 2011-01-01 at 16:40
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