Thread for posting tiny primes

[3.14159]

Originally Posted by Charles

So the category (and any other that uses the term "general") are ill-defined.

General cofactor is still defined, as I fixed the definition. There was no issue with special cofactor, however.

[science_man_88]

Originally Posted by CRGreathouse

So the category (and any other that uses the term "general") are ill-defined.

glad that's settled now on to the next argument right

[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.

But all numbers are k-b-b, right?

[3.14159]

Originally Posted by Charles

But all numbers are k-b-b, right?

Nope. Remember the restrictions we placed on k-b-b's? Either b can't be 1, or k < b^b

You corrected the OEIS sequences for each of these.

You could say every 4n + 1 number is a k-b-b, and that would be valid.

[CRGreathouse]

Originally Posted by 3.14159

Nope. Remember the restrictions we placed on that? Either b can't be 1, or k < b^b

I remember that you made sequences of k-b-b primes with those restrictions, but you didn't mention which, if any, restrictions applied here.

But even that doesn't work. Your second example from #393, 348487007766634158834636277, is a k-b-b with b not equal to 1.

Edit: You edited this in after I quoted you.

Originally Posted by 3.14159

You could say every 4n + 1 number is a k-b-b, and that would be valid.

So primes of the form 4n+1 are not general numbers? Likewise, the residues 1, 5, 9, 13, 17, 21, 25, 28, 29, 33, 37, 41, 45, 49, 53, 55, 57, 61, 65, 69, 73, 77, 81, 82, 85, 89, 93, 97, 101, and 105 mod 108 are all bad?

[3.14159]

Originally Posted by Charles

But even that doesn't work. Your second example from #393, 348487007766634158834636277, is a k-b-b with b not equal to 1.

With no k < b^b restrtiction and b > 1, it is still not identical to the 4n + 1 numbers.

[Mathew]

In 376 3.14159 states the second largest prime is by 3.14159. This is referring to a PRP 3.14159 found in this thread 237 3.14159 then proceeds to abandon, since there are "no simple methods." In post 240 I show that prime testing can be done and prove 3.14159's PRP is in fact prime.

3.14159 your thoughts

[CRGreathouse]

Originally Posted by 3.14159

With no k < b^b restrtiction and b > 1, it is still not identical to the 4n + 1 numbers.

I don't know what "it" refers to here, but 348487007766634158834636277 (one of your examples from post #393) is a member of A175768, as are 11 of your 16 examples there. But by post #405 (even as softened by #411), these are no longer considered general numbers.

[science_man_88]

Originally Posted by CRGreathouse

But all numbers are k-b-b, right?

well for k>=0 and b=1 I can see how this would work for all positive integers.

0*1^1+1 = 0+1 = 1
1*1^1+1 = 1+1 = 2
2*1^1+1 = 2+1 = 3
.
.
.
.
.


anyway you get the point can't get it to work to be negative unless k or b is negative that I know of.

[3.14159]

Originally Posted by Charles

I don't know what "it" refers to here, but 348487007766634158834636277 (one of your examples from post #393) is a member of A175768, as are 11 of your 16 examples there. But by post #405 (even as softened by #411), these are no longer considered general numbers.

And it is correct. These are k-b-b's under the second definition. But not under the first.

[CRGreathouse]

Originally Posted by 3.14159

And it is correct. These are k-b-b's under the second definition. But not under the first.

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?