1000 Bottles, One Poisoned

Level 6●●●●○ Hard~7 min

Problem

A king has 10001000 bottles of wine; exactly one is poisoned. The poison is lethal in any dose but takes effect only after 2424 hours, with no other symptoms. The king has prisoners he can use as testers and needs to identify the poisoned bottle within 2424 hours (one round of tasting). What is the minimum number of prisoners required?