Answer: 180,396,380,815,100,901,214,157,639 — wait, for 100 steps: 180,396,380,815,100,901,214,157,639
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Answer: No such number exists — the trap IS the puzzle! Largest possible product falls short.
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Answer: 101 (since 10²⁶ + 1 = (10²)¹³ + 1, and 101 divides 10² + 1 = 101)
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