Arithmetic Sequence of 16 Primes

Theorem
The $16$ integers in arithmetic sequence defined as:
 * $2\,236\,133\,941 + 223\,092\,870 n$

are prime for $n = 0, 1, \ldots, 15$.

Proof
First we note that:


 * $2\,236\,133\,941 - 223\,092\,870 = 2\,013\,041\,071 = 53 \times 89 \times 426\,763$

and so this arithmetic sequence of primes does not extend to $n < 0$.

But note that $2\,236\,133\,941 + 16 \times 223\,092\,870 = 5\,805\,619\,861 = 79 \times 73\,488\,859$ and so is not prime.