Logan's Wacky Number Puzzle
During Practice for the upcoming MAO Competition, Logan decides to ask Sanjoy a Number Puzzle:
1.) "I am a number A. I am the largest two-digit prime number in base 10. I am the atomic number of an actinide."
2.) "I am a number B. I am the sum of three consecutive cubes. In addition I am a Kaprekar Number, and I am the atomic number of an actinide."
Find the Product of A and B.