- Could anyone explain, in simplistic terms, were that possible, how Legendre(?) proved that primes appearing in an arithmetic progression, continue to appear, with no limit.

Alas I cannot find the proof on-line, and I doubt I would understand it, so a Terence Tao like explanation, would really be welcomed.

Thanks

Bob

Sent from Samsung tablet - --- In primenumbers@yahoogroups.com,

Bob Gilson <bobgillson@...> wrote:

> Alas I cannot find the proof on-line

Dirichlet's proof is here:

http://tinyurl.com/3ef2l4o

David - --- In primenumbers@yahoogroups.com,

"djbroadhurst" <d.broadhurst@...> wrote:

> Dirichlet's proof is here:

For a modern account, in English, see

> http://tinyurl.com/3ef2l4o

http://www.math.uga.edu/~pete/4400DT.pdf

where Pete Clark remarks:

"One of the amazing things about the proof of Dirichlet's theorem

is how modern it feels. It is literally amazing to compare the

scope of the proof to the arguments we used to prove some of the

other theorems in the course, which historically came much later.

...

Let us be honest that the proof of Dirichlet's theorem is of

a difficulty beyond that of anything else we have attempted in

this course."

I remark that Selberg's "elementary proof" is also rather

difficult. It is elementary only in the sense that

he does not use complex characters or infinite sums:

http://www.jstor.org/pss/1969454

David - This proof is awesome!!!

Way too complicated for what it applies, but way too rich for the limits it implies!

________________________________

From: djbroadhurst <d.broadhurst@...>

To: primenumbers@yahoogroups.com

Sent: Thursday, September 1, 2011 7:46:15 PM

Subject: [PrimeNumbers] Re: Infinite Primes in an Arithmethic Progression

--- In primenumbers@yahoogroups.com,

"djbroadhurst" <d.broadhurst@...> wrote:

> Dirichlet's proof is here:

For a modern account, in English, see

> http://tinyurl.com/3ef2l4o

http://www.math.uga.edu/~pete/4400DT.pdf

where Pete Clark remarks:

"One of the amazing things about the proof of Dirichlet's theorem

is how modern it feels. It is literally amazing to compare the

scope of the proof to the arguments we used to prove some of the

other theorems in the course, which historically came much later.

...

Let us be honest that the proof of Dirichlet's theorem is of

a difficulty beyond that of anything else we have attempted in

this course."

I remark that Selberg's "elementary proof" is also rather

difficult. It is elementary only in the sense that

he does not use complex characters or infinite sums:

http://www.jstor.org/pss/1969454

David

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