Has to be consecutive. The current series (17) doesn't count. Specials don't count. If Paul Hollywood is involved in series 18, 19, and 20, resolves YES. Otherwise NO.

(Obviously if he does more than 3 series, resolves YES.)

If it moves to a different channel and keeps the same name, that's the same show, so Hollywood would need to move with it for a YES resolution. If it moves to a different channel and he keeps doing a different baking show, that doesn't count.