What is the product of the two largest one-digit primes and the largest two-digit prime?
The two largest one-digit primes are 5 and 7; the largest two-digit prime is 97 (98 and 99 are both composite).  The product of these three primes is $5 \cdot 7 \cdot 97 = 35 \cdot 97 = 35(100-3)=3500-105=\boxed{3395}$.