> I find this to be a huge result way bigger than say Wiles proof of FLT

Well I see your point, the proof of FLT is a little complex for most

> because that proof will never

> be understood by more than a few people. Besides, it was based on another

> conjecture on modular

> forms which under certain conditions implied the truth of FLT and Wiles

> proved that little result.

people. But that point of view could also be said to de-value the

achievments of some of the more "detailed" results on primes in A.P.'s

> I am not meaning to fix n and vary a and k. I want to vary all three a,k,n.

Well no, it was just unclear what you wanted to vary when. Fixing *any*

>

> Is there only one k and a for which the statement is true?

k and a with (k,a)=1, and varying only n, you get infinitely many

primes.

> for k =0 and a =1 we have for n=0,1,2,...,0n+1

Well do you think this sequence contains infinitely many primes? Of

> 1,1,1,1,1,1,1,1,1,...

course not. Every integer divides zero. Or perhaps no integer divides

zero. Is zero an integer? Anyway, you can't say that (0,1)=1.

Dirichlet's proof depended on the characters modulo k. If k=0, there are

no characters, and therefore the proof fails.

Andy>From: Andy Swallow <umistphd2003@...>

It is as easy to de-value as it is to criticize.

>To: primenumbers@yahoogroups.com

>Subject: Re: [PrimeNumbers] Re: Primes in the concatenation with the digits

>of Pi

>Date: Tue, 3 Feb 2004 10:21:21 +0000

>

>

> > I find this to be a huge result way bigger than say Wiles proof of FLT

> > because that proof will never

> > be understood by more than a few people. Besides, it was based on

>another

> > conjecture on modular

> > forms which under certain conditions implied the truth of FLT and Wiles

> > proved that little result.

>

>Well I see your point, the proof of FLT is a little complex for most

>people. But that point of view could also be said to de-value the

>achievments of some of the more "detailed" results on primes in A.P.'s

>

Does this mean you now agree that the infinitude of primes can be

> > I am not meaning to fix n and vary a and k. I want to vary all three

>a,k,n.

> >

> > Is there only one k and a for which the statement is true?

>

>Well no, it was just unclear what you wanted to vary when. Fixing *any*

demonstrated by Dirlichlet's

theorem? How about the 6n+1 and 6n+5 argument which you do not address?

>k and a with (k,a)=1, and varying only n, you get infinitely many

Well, while 6n+4 does not satisfy the Dirichlet criteria, I can combine it

>primes.

>

> > for k =0 and a =1 we have for n=0,1,2,...,0n+1

> > 1,1,1,1,1,1,1,1,1,...

>

>Well do you think this sequence contains infinitely many primes? Of

>course not. Every integer divides zero. Or perhaps no integer divides

with all the

(k,a) = 1 sets if I so desire as I did with 0n+1 just to complete the

integers formed by the

second term. This was redundancy. But redundancy is allowed as in the two

sets 2n+1 and 3n+1

where there are repeated numbers. It could well have been left out since 1

is not prime anyway

and the infinite dirichlet produced set of second terms of the rows formed

by

1n+1 -> 2

2n+1 -> 3

3n+1 -> 4

...

...

was sufficient to prove my point. Well, had I done that some of your thunder

would have been

calmed.:-)

>zero. Is zero an integer? Anyway, you can't say that (0,1)=1.

True. However, this does not preclude me to combine the progression 0n+a

>Dirichlet's proof depended on the characters modulo k. If k=0, there are

>no characters, and therefore the proof fails.

with the

Dirichlet allowed ones. 0n+7 would produce infinitly many primes albiet not

necessarily different.

My statement still stands:

You can prove that there is an infinite number of primes using Dirichlet's

theorem. Moreover,

you can prove the infinitude in a infinite number of ways. well, if you have

time and space.

Have fun,

Cino

_________________________________________________________________

Let the new MSN Premium Internet Software make the most of your high-speed

experience. http://join.msn.com/?pgmarket=en-us&page=byoa/prem&ST=1> My statement still stands:

Dirichlet's theorem proves that there are an infinite number of primes

>

> You can prove that there is an infinite number of primes using

> Dirichlet's theorem.

in certain infinite subsets of the integers. So the fact that the

total number of primes is infinite follows immediately...

Apologies if I misunderstood your original message and its'

intentions.

Andy