## Question

Let *P* be a prime number such that *P* ≥ 23. Let *n* = *p*! + 1. The number of primes in the list *n* + 1, *n* + 2, *n* + 3, … *n + p* – 1 is

### Solution

0

For 1 ≤ *k* ≤ *p* – 1, *n + k = p*! + *k* + 1, is clearly divisible by *k* + 1. Therefore, there is no prime number in the given list.

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