【Question 2】
A prime number $a$ is 10 less than a perfect square $b$, then the minimum value of $a$ is $\qquad$. (Note: A perfect square is a number that can be expressed as the square of an integer, for example $4=2^{2}, 9=3^{2}$, so $4$ and $9$ are both perfect squares.)
【Analysis and Solution】
Number Theory, Prime Numbers, Perfect Squares.
If $a=2$, then $b=2+10=12$ is not a perfect square;
Therefore, $a$ is an odd number, then $b=a+10$ is also an odd number, and $b$ is the square of an odd number;
The odd perfect squares greater than 10, in ascending order, are $5^{2}=25, 7^{2}=49, 9^{2}=81, \ldots \ldots$;
$25-10=15=3 \times 5$ is a composite number,
$49-10=39=3 \times 13$ is a composite number,
$81-10=71$ is a prime number;
Therefore, the smallest $a$ is 71.