Solution:

The $n$th term consists of $n$ ones, then a $2,$ then $n$ ones. It factors as a repunit times a number of the form $10^n + 1:$ $$121 = 11 \cdot 11, \quad 11211 = 111 \cdot 101, \quad 1112111 = 1111 \cdot 1001,$$ and in general the $n$th term equals $\underbrace{1\cdots1}_{n+1} \cdot (10^n + 1).$

For every $n \ge 1$ both factors exceed $1,$ so every term is composite. None of the ten numbers is prime.

Thus, the correct answer is A.