Re: Least primes in arithmetic progressions

Geevarghese Philip <gphilip.newsgroups@xxxxxxxxx> writes in article <pan.2005.12.14.03.12.01.749723@xxxxxxxxx> dated Wed, 14 Dec 2005 22:48:37 +0500:
>On Tue, 13 Dec 2005 09:55:33 +0200, Risto Kauppila wrote:
>
>> Let p be be a prime. By Dirichlet's theorem there exists
>> least positive integer n for which f(p) = np+1 is prime.
>
>How by Dirichlet's theorem? Does the same argument also stick for f(n) =
>np, which we know is never a prime?

Dirichlet's theorem states that the series a*n+b contains an infinite number
of primes, provided gcf(a,b)=1.

gcf(p,0)=p, so the case b=0 is excluded.

gcf(p,1)=1

--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
.

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