I tried to find good cyclotomic polynomials for producing primes and I maximized the smallest possible prime factor divided by the number of the cyclotomyc polynomial. The results are summarized in the following table :
1st entry : The number $n$ of the cyclotomic polynomial
2nd entry : The smallest possible prime factor of $\phi_n(b)$
3rd entry : The number of primes for $b\le 10^5$
4th entry : The number of digits of the largest prime for $b\le 10^5$
@MartinHopf I counted the number of primes in some ranges for $\phi_n(n+k)$. $k=-21$ seems to be the champion , at least for $-100\le k\le 100$ . Any idea why ?
