Statement 1 is insufficient. Statement 1 tells us that $n$ is a prime number, meaning $n$ could be one of the following: 11, 13, 17, or 19. However, this does not provide a unique value for $n$, so Statement 1 alone is insufficient to answer the question.

Statement 2 is insufficient. Statement 2 tells us that when $n$ is divided by 4, the remainder is 1. This means $n$ could be 13 or 17, but this does not provide a unique value for $n$ either. Therefore, Statement 2 alone is insufficient to answer the question.

Statements 1 and 2 together: Insufficient. Combining both statements, we get two possible values for $n$: 13 and 17. Since we still have two possibilities, the statements together are insufficient to determine a unique value for $n$.