A prime number $a$ is 10 less than a perfect square number $b$, then the minimum value of $a$ is $\qquad$ (Note: A perfect square number 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 square numbers)
Number Theory, Prime Numbers, Perfect Squares
If $a=2$, then $b=2+10=12$ is not a perfect square
Therefore, $a$ is odd, then $b=a+10$ is also odd, and $b$ is the square of an odd number
The odd perfect squares greater than 10, from smallest to largest, are $5^{2}=25, 7^{2}=49, 9^{2}=81, \ldots$
$25-10=15=3 \times 5$ 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