Happy Prime Year MMXI!

ATH · 2010-12-31, 21:40

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/

Mini-Geek · 2010-12-31, 22:57

Quote:

Originally Posted by ATH

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

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.

petrw1 · 2011-01-01, 05:59

count down with me....

davieddy · 2011-01-01, 07:36

Quote:

Originally Posted by petrw1

count down with me....

-359,-360,-361....

ixfd64 · 2011-01-01, 08:04

Unfortunately, 2010 was a dry year, in the context of new Mersenne primes. Let's hope that 0b11111011011 will really be a "prime" year!

davieddy · 2011-01-01, 08:28

Quote:

Originally Posted by Mini-Geek

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

Merfighters · 2011-01-01, 09:21

Quote:

Originally Posted by petrw1

count down with me....

-65980, -65981, -65982, ...

Also the 2011th prime is 17483.

Mini-Geek · 2011-01-01, 12:29

Quote:

Originally Posted by davieddy

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.

davieddy · 2011-01-01, 16:05

Quote:

Originally Posted by Mini-Geek

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"?

Mr. P-1 · 2011-01-01, 16:35

[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.

davieddy · 2011-01-01, 16:39

...from either 10 or 11 years ago,

Happy 202nd decade to y'all

David

2010-12-31, 21:40	#1
ATH Einyen Dec 2003 Denmark 3×17×59 Posts	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/

2011-01-01, 05:59	#3
petrw1 1976 Toyota Corona years forever! "Wayne" Nov 2006 Saskatchewan, Canada 23×197 Posts	1 minutes to go here..... count down with me....

2011-01-01, 16:39	#11
davieddy "Lucan" Dec 2006 England 1100101001010₂ Posts	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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2011-01-01, 08:04	#5
ixfd64 Bemusing Prompter "Danny" Dec 2002 California 2345₁₀ Posts	Unfortunately, 2010 was a dry year, in the context of new Mersenne primes. Let's hope that 0b11111011011 will really be a "prime" year!

2011-01-01, 16:35	#10
Mr. P-1 Jun 2003 7×167 Posts	[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.