Puzzle: Banter

Engineering

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Puzzle: Banter

Engineering

Greg says, “I’ll tell Phil the product of two integers, each of which is greater than one, and Sean their sum.”
After Greg whispers to both of them, Phil shrugs, “I don’t know Greg’s numbers.”
“I already knew that,” Sean states.
“But now I do!” Phil exclaims.
Sean smirks, “Well then so do I.”

What might Greg’s integers be?