Slimes do not despawn unless the player moves 128 blocks away. Unlike other mobs, slimes never despawn if there is a player within this range; they are unaffected by normal despawn behavior.

Steps to reproduce:

1. Spawn a slime and a zombie (for a control group). Place blocks around them to make sure they don't move anywhere.

2. Go around 64 blocks away.

3. Wait a few minutes.

The zombie will almost certainly have despawned by this time; if it is over 32 blocks from the player, it has a chance of despawning each game tick. However, the slime will not despawn, no matter how long the player waits; it only despawns when the player leaves the area.