Question 10
Determine the number of non-negative integers $M$ satisfying exactly three of the following four statements:
1. $M$ is prime.
2. $M+3$ is prime.
3. $1\lt \sqrt M\lt 8$.
4. $M+5$ has an odd number of factors.
**Answer format:** Enter the count of admissible integers, not one example of $M$. Factors mean positive integer divisors; 1 is not prime.
1. $M$ is prime.
2. $M+3$ is prime.
3. $1\lt \sqrt M\lt 8$.
4. $M+5$ has an odd number of factors.
**Answer format:** Enter the count of admissible integers, not one example of $M$. Factors mean positive integer divisors; 1 is not prime.