Colbert Numbers

[jjjjL]

Science has decided!

See our homepage for details about the newest inspiration for running SB: finding the remaining Colbert Numbers!

http://www.seventeenorbust.com/


Cheers,
Louie

[wolfemancs]

I think there's an error in the content accessed by one of the links you posted in the news post. On http://primes.utm.edu/glossary/xpage/ColbertNumber.html it says:
"Waclaw Sierpinski used modular covers to prove there were infinitely many odd integers k for which k*2^n+1 are prime for all n > 1. It has been conjectured that 78557 is the smallest . . ."

Shouldn't it say that there are infinitely many odd integers k for which k*2^n+1 are COMPOSITE for all n > 1?

[jjjjL]

I think there's an error in the content accessed by one of the links you posted in the news post. On http://primes.utm.edu/glossary/xpage/ColbertNumber.html it says:
"Waclaw Sierpinski used modular covers to prove there were infinitely many odd integers k for which k*2^n+1 are prime for all n > 1. It has been conjectured that 78557 is the smallest . . ."

Shouldn't it say that there are infinitely many odd integers k for which k*2^n+1 are COMPOSITE for all n > 1?

The reference is surprisingly correct. That's one of the most interesting thing, that there should be so many Sierpinski Numbers.... infinite even. SB is just proving conclusively which is the smallest. By finding the required Colbert Numbers.

Cheers,
Louie

[wolfemancs]

Hmmm. . . by looking for the Colbert numbers, aren't we looking for prime numbers? With the reasoning that finding a single prime for each of the remaining k values, we prove that k*2^n+1 is Not COMPOSITE for all n, thereby proving that 78,557 is the lowest k for which k*2^n+1 is COMPOSITE for all n?

[jjjjL]

Hmmm. . . by looking for the Colbert numbers, aren't we looking for prime numbers? With the reasoning that finding a single prime for each of the remaining k values, we prove that k*2^n+1 is Not COMPOSITE for all n, thereby proving that 78,557 is the lowest k for which k*2^n+1 is COMPOSITE for all n?

Haha... I'm dumb.

My mind wouldn't allow me to believe that anything Chris Caldwell wrote and/or read could possibly be wrong so I totally missed your point. Sorry. I'm pretty sure you're right now after re-reading it again.

Obviously there aren't any known k values for which ALL n > 1 are prime, or you could generate arbitrarily large prime numbers by just plugging large n values in. EFF prizes here we come! ... so yeah, you've convinced me now. Thanks for not giving up on me.

Let me contact Chris and get that updated. Thanks!

Cheers,
Louie

[Deciheximal]

Want more number crunchers? Marketing, marketing, marketing! I love it.

So who gets credit for the idea?

[jjjjL]

So who gets credit for the idea?

My girlfriend. A lot of mathematicians agree that it's a good name too though. So we've gone ahead and set up the new definition.

Hopefully the Colbert nation will get wind of it. We can't wait to uncover the next Colbert Number so that we may honor Stephen Colbert!

Cheers,
Louie

[wolfemancs]

A friend of mine asked an interesting question about the definition of Colbert numbers.

Were a second prime to be found for any of the already completed k values, or 2 primes found for the k values currently being tested, would only the first found classify as a Colbert Number (because it's the only one that helps prove the theorem), would both numbers be Colbert numbers (because either of them could be used in the proof of the theorem)?

[jjjjL]

A friend of mine asked an interesting question about the definition of Colbert numbers.

Were a second prime to be found for any of the already completed k values, or 2 primes found for the k values currently being tested, would only the first found classify as a Colbert Number (because it's the only one that helps prove the theorem), would both numbers be Colbert numbers (because either of them could be used in the proof of the theorem)?

Only the first number would be required so only it would be a Colbert Number. Otherwise there would be an infinite amount of them. There is particular significance that there are only 11.


Cheers,
Louie

[Drakull]

Hopefully the Colbert nation will get wind of it. We can't wait to uncover the next Colbert Number so that we may honor Stephen Colbert!

What if the person finding the number doesn't like Colbert???

[opyrt]

What if the person finding the number doesn't like Colbert???

Or is from a country that is not USA?
I've never heard about the person before, but that does not prevent me from wanting to find primes!