Primes of form k*n+1

[Max]

On 2/17/06, Klaus Brockhaus <klaus-brockhaus at t-online.de> wrote:

> In the OEIS there are a few sequences of the type
>         Primes of form k*n+1
> or equivalently
>         Primes congruent to 1 (mod k)
> for fixed positive integer k,
> e.g. A002476 for k=3 and k=6, A002144 for k=4, A030430 for k=5 and k=10, A007519 for k=8, A061237 for k=9, A068228 for k=12.
> In none of these entries the infiniteness of the sequence is mentioned as a problem, so I suppose that it is (a consequence of) an elementary or well-known theorem.

That's Dirichlet Theorem: http://mathworld.wolfram.com/DirichletsTheorem.html

> And what is known about the density of such sequences relative to all primes (A000040)?

See http://mathworld.wolfram.com/ModularPrimeCountingFunction.html

Max