Number Theory, or Logic?

First number of the sequence is the $(1^2+1)$ 'th or the $2$ nd prime, which is $3$ . Second number is the $(2^2+1)$ 'th or the $5$ th prime, which is $11$ , and so on. Hence the sixth number is the $(6^2+1)$ 'th or the $37$ th prime, which is $\boxed {157}$