[QUOTE=3.14159;228915]It seems as if every integer has an interesting property or two.[/QUOTE]

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?

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.

[QUOTE=science_man_88;228950]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.[/QUOTE]

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

[QUOTE=wblipp;228949]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?[/QUOTE]
"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. :smile:

[QUOTE=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?
[/QUOTE]

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

[QUOTE=3.14159;228958]It is a k-b-b prime when k is not restricted and where b > 1.[/QUOTE]

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

What range restrictions do you make on the others?

[QUOTE=Charles]So 4n + 1 aren't allowed as "general" primes?
[/QUOTE]

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

Refuting a potential complaint:

[QUOTE=Post #276][B]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.[/B]
[/QUOTE]

k * 2[sup]2[/sup] + n is allowed. But your number k better be large.

Try k * 2[sup]6655[/sup] + n. You wouldn't need an unnecessarily large k or n.

801 * 2[sup]26300[/sup] + 8488172602847190089021 (7920 digits)

[QUOTE=3.14159;228966][QUOTE=3.14159;228545]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.[/QUOTE]

k * 2[sup]2[/sup] + n is allowed. But your number k better be large.[/QUOTE]

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

[QUOTE=CRGreathouse;228971]With that definition, I'd love to see a primes greater than 10^1999 that [i]doesn't[/i] qualify for #19. Does such a prime exist?[/QUOTE]

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.

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.

[QUOTE=3.14159;228922]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.[/QUOTE]

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