Sphinx's Riddle (Part 2)

Logic Level 4

After solving the puzzle in the last Sphinx's Riddle, you were facing yet another Sphinx guarding another exit portal. (It was indeed a complex pyramid!)

Once more, there were 9 stone tablets arranged in a \(3\times 3\) square, and behind each tablet hid a distinct digit from 1-9 inclusively. Like before, you had to answer every number correctly; otherwise, you'd be eaten alive!

Then the Sphinx gave you 3 clues for the 3 rows of the square:

Clue for Row #1: \(A\) is prime. The 2-digit \(\overline{AB}\) is prime. The 3-digit \(\overline{ABC}\) is prime and is the sum of a cube and \(\overline{AB}\).

Clue for Row #2: \(D\) is composite. \(\overline{DE}\) is composite. \(\overline{DEF}\) is the difference between two squares.

Clue for Row #3: \(G\) is a perfect square. \(\overline{GH}\) is a perfect square. \(\overline{GHI}\) is the sum of two different squares.

What is the value of the 9-digit integer \(\overline{ABCDEFGHI}\)?


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