Determining if a Positive Integer is Prime

Hard Data Sufficiency Analyzing Information

Let $x$ represent a positive integer. We want to determine whether $x$ is a prime number.

Statement (1): $x$ is not divisible by any prime number less than $x$.

Statement (2): $x$ is greater than 2.

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

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