The King's Poisoned Wine

The problem
1,000 bottles · exactly one poisoned · 24 hoursminimum prisoners as tasters?

A king has 1,000 bottles of wine for tomorrow night's banquet. He just learned that exactly one is poisoned. The poison takes 24 hours to act, then kills. The banquet is in 24 hours.

The king has prisoners he can use as tasters. Each prisoner can drink from any combination of bottles. After 24 hours, prisoners who drank from the poisoned bottle die.

What's the minimum number of prisoners needed to guarantee identifying the poisoned bottle in time?