**Question:**

Let be the largest integer not greater than . How many numbers of integer are there such that are prime number?

**Answer:**

Since a set of integers can be expressed as the forms,

Then we have 3 cases to consider,

Case 1,

Since p is prime,

Case 2,

Since p is prime,

Case 3,

Since p is prime, k has no solution.

Therefore, the only possible integers n are 3 or 4.

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