MathNet 2023-part-05 — 191 problems (EN–VI) Question 99

For every positive integer $n$ define $a_n = n + 1$, $b_n = 2 \cdot n + 3$, $c_n = 3 \cdot n + 5$, $d_n = 4 \cdot n + 7$. Find all positive integers $n$ which have at most two digits and $a_n, b_n, c_n$, and $d_n$ are prime.