【Question 8】
Given that $A$ is a prime number less than 100, and $A+10, A-20, A+30, A+60, A+70$ are all prime numbers, then $A=$ $\qquad$.(List all possible numbers)
【Analysis and Solution】Number Theory, Prime Numbers.
$$
\begin{array}{l}
A+10 \equiv A-20 \equiv A+70 \equiv A+1(\bmod 3) ; \\
A+30 \equiv A+60 \equiv A(\bmod 3) ;
\end{array}
$$

Obviously, $A+1$ and $A$ cannot be multiples of 3;

Thus, $A \equiv 1(\bmod 3)$;
Prime numbers greater than 20 and less than 100 are: $23,29, 31,37,41,43, 47, 53, 59, 61, 67, 71,73, 79, 83, 89, 97$; Among these, those that satisfy $\bmod 3$ with a remainder of 1 are: $31, 37, 43, 61, 67, 73, 79, 97$;

Check each one:
$$
\begin{array}{l}
31+60=91=7 \times 13 ; 61+30=91=7 \times 13 ; \\
67+10=77=7 \times 11 ; 73+70=143=11 \times 13 ; 97-20=77=7 \times 11 ;
\end{array}
$$

Therefore, $A=37,43,79$.