The Grand Princess Carries 2,600 passengers. However the size of the ship must be taken into consideration too, the Grand Princess is 109,000 gross tons. So each passenger will have more room than if they travelled on a 80,000 ton ship. (NCL's Pearl for example carries 2,394 guests and is only 93,558 tons.
Between 2,600 and 3,100 the latter being unlikely as it would mean that every bed and bunk would be filled. That is the maximum but could sail with less....Neil .
The grand princess has 2,600 passengers.