[seqfan] Primes of the form kn+1

[Michael Porter]

Is it true that for every positive integer n, there is a prime of the form kn+1 with 1<=k<=n?

I submitted the following PARI program for sequence A089727:
A089727(n) = {local(k);k=n;while(!isprime(n*k+1),k--);n*k+1}
and then I started wondering if the while loop would always terminate.

Thanks,
Michael