Smallest 10 Primes in Arithmetic Sequence

Theorem
The smallest $10$ primes in arithmetic progression are:
 * $199 + 210 n$

for $n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9$.

These are also the smallest $8$ and $9$ primes in arithmetic progression.

Proof
But note that $199 + 9 \times 210 = 2299 = 11^2 \times 19$ and so is not prime.