Thread for posting tiny primes

[wblipp]

Originally Posted by 3.14159

It seems as if every integer has an interesting property or two.

This is a well known fact that was alluded to on another thread recently. It's proven by contradiction. Remove all the interesting numbers - primes, powers, mersennes, proths, whatever else is interesting. Of all the remaining numbers, there must be a smallest one. Isn't that interesting?

[science_man_88]

sounds to me like k-b-b prime = general number prime I could be wrong and has no other special form. I'm not sure of anything though.

[CRGreathouse]

Originally Posted by science_man_88

sounds to me like k-b-b prime = general number prime I could be wrong and has no other special form. I'm not sure of anything though.

See Pi's comment here:
http://oeis.org/classic/A175768
and my earlier comment to that effect one of the threads.

[Mini-Geek]

Originally Posted by wblipp

This is a well known fact that was alluded to on another thread recently. It's proven by contradiction. Remove all the interesting numbers - primes, powers, mersennes, proths, whatever else is interesting. Of all the remaining numbers, there must be a smallest one. Isn't that interesting?

"interesting" is poorly defined.
That assumes that if the first smallest not-otherwise-interesting number is interesting, then the rest will be as well. What if your definition of interesting only counts the first 0, (i.e. none) or 1, (i.e. "the first one counts, but after that no") or 20 (i.e. "ok we can list many of the starting ones, but no more after that for that reason, even if you want to call it another category") smallest not-otherwise-interesting numbers? Then there can be a smallest not-otherwise-interesting number that isn't interesting for that reason.

[3.14159]

Originally Posted by Charles

I don't know what this "it" refers to, either. Are you saying that you're only excluding k-b-b primes that are in the intersection of A180362 and A175768, that is, A180362?

It is a k-b-b prime when k is not restricted and where b > 1.

[CRGreathouse]

Originally Posted by 3.14159

It is a k-b-b prime when k is not restricted and where b > 1.

So 4n + 1 aren't allowed as "general" primes?

What range restrictions do you make on the others?

[3.14159]

Originally Posted by Charles

So 4n + 1 aren't allowed as "general" primes?

General arithmetic progressions; provided they are at least 2k digits in size, and where exponent n is greater than 1.

Refuting a potential complaint:

Originally Posted by Post #276

19. General arithmetic progressions, k * b^n + c, where c is a prime > 10^2, where the prime is at least 2000 digits in length, and where the exponent n > 1.

k * 2² + n is allowed. But your number k better be large.

Try k * 2⁶⁶⁵⁵ + n. You wouldn't need an unnecessarily large k or n.

801 * 2²⁶³⁰⁰ + 8488172602847190089021 (7920 digits)

[CRGreathouse]

Originally Posted by 3.14159

k * 2² + n is allowed. But your number k better be large.

With that definition, I'd love to see a primes greater than 10^1999 that doesn't qualify for #19. Does such a prime exist?

[science_man_88]

Originally Posted by CRGreathouse

With that definition, I'd love to see a primes greater than 10^1999 that doesn't qualify for #19. Does such a prime exist?

well disqualified forms wouldn't but if k=2.5*10^1999 then for b^b=2^2

any n that gives a prime that isn't disqualified is submittable.

[CRGreathouse]

I'm not sure what you're saying. Do you have an example of a prime larger than 10^1999 which does not qualify for #19?*

* Or should I say, #19 as of 07 Sep 10 08:41 PM, since these definitions are fairly malleable.

[CRGreathouse]

Originally Posted by 3.14159

If it's not a Proth/Generalized Proth/k-b-b/Fermat/Generalized Fermat/Cullen-Woodall/Generalized Cullen-Woodall/Mersenne/Fibonacci/Lucas/Generalized Fibonacci, it's a general number.

When you get a chance, would you define these terms and the ranges to which they apply?