[Number Theory]
Problem: Define a reverse prime to be a positive integer $N$ such that when the digits of $N$ are read in reverse order, the resulting number is a prime. For example, the numbers 5, 16, and 110 are all reverse primes. Compute the largest two-digit integer $N$ such that the numbers $N, 4 \cdot N$, and $5 \cdot N$ are all reverse primes.

Solution: Because $N<100,5 \cdot N<500$. Since no primes end in 4, it follows that $5 \cdot N<400$, hence $N \leq 79$. The reverses of $5 \cdot 79=395,4 \cdot 79=316$, and 79 are 593,613 , and 97 , respectively. All three of these numbers are prime, thus 79 is the largest two-digit integer $N$ for which $N$, $4 \cdot N$, and $5 \cdot N$ are all reverse primes.

Final answer: 79