The twenty-four pound smoothbore cannon was the strongest brand of cannon during the Age of Sail, and can be found on the strongest ships out on the caribbean; mostly aboard Treasure Fleets, Ship of the Lines, certain Hunters and EITC Juggernaut class war frigates.
The Flagship in Lawrence's Fleet of three ships. All broadside cannons consist of these cannons, salvaged from sunken EITC Juggernaut class war frigates, while the remaining deck guns remain the standard twelve pound. Rumor is he has more stashed away on some island, but the map to their location was burned during the Raid of Cadiz, Spain.
The Harkaway, Jolly Rogers Flagship, is known to hold an entire broadside of these powerful Cannons. All cannons used on the ship are rumored to be 24 pounders. Juggernauts may be tough, but not as tough as this, for Jolly installed a special feature: The cannons are equipped with Green Skulls which power-up the cannons, making this ship almost invincible.
The Green Runner.
The Green Runner is known to have picked up 10 of these guns. The 4 bow cannons are 24 pounders, and so are 3 on each broadside. This is thought to be why The Runner survived against Jolly Roger in the Goldvane Trilogy.