--- rlberry2002 <

rlberry2002@...> wrote:

> Please pardon my ignorance; I am here to learn to grow in my

> knowledge of number theory. However, I will try to be more careful

> in responding to posts before I have fully thought out my response

> - you could extend me the same courtesy.

I would trust that such courtesy is demonstrated on the list.

(Yeah, flame me off list, you won't be the first... (or the second)

:-) )

> Your example of N=2^p + 12213 violates one of the two

> qualifications

> that I laid down - "the equation cannot be reducible".

Strictly, it is irreducible. The letter of the law is obeyed.

> I typically

> would use this tenet for an equation like 4n + 1 (which does have

> infinitely many primes in it)where n is odd. The tenet holds for

> numbers of the form 2^p + n also, it just is usually harder to find

>

> the pattern that this type of equation reduces to. In your

> example,

> you provide the pattern which violates my first condition: that is

>

> for 2, 3, 1 Mod 12, 5 Mod 12, 7 Mod 12, & 11 Mod 12; there a fixed

> set of possible outcomes each of which will have fixed factors

> depending upon which of the outcomes it fall under.

Sure, but that's not redicibility. What Jack has highlighted is an

intrinsically interesting property about that sequence of numbers.

This property will ba shared by an infinite number of other

sequences, not just the ...+12213. The property isn't reducibility,

and that term was used, it's a very precisely defined term, so Jack

and others can't be faulted for taking the term at face falue.

Perhaps the term "with no intrinsic predicatble factorisations" or

similar could be used to cover such concepts.

Such forms are certainly vastly interesting, the Sierpinski/Riesel

problems (that Jack mentioned, IIRC) are all about whether there are

primes with forms that have no intricsic predictable factorisations.

(hmmm, reminder to self or others - is there a link waiting to be

added to the yahoogroup regarding the Sierpinski/Riesel problems?)

Phil

__________________________________________________

Do You Yahoo!?

Yahoo! Health - your guide to health and wellness

http://health.yahoo.com