I have been trying to google this but couldn't find anything relevant.

On a dos disk, if you delete a primary partition, the numbering of other partitions is not affected. If you then create a new primary partition, it gets the same number as the one you deleted, regardless of its location on the drive. With logical disks however, deleting a partition makes the other numbers close up, which affects your bootloader and fstab.

What happens when you delete a primary partition on a gpt disk?

As with msdos MBR primnary partitions, the numbering of the other GPT partitions will not change.

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In a nutshell, a legacy MBR(DOS) partition table has 4 entries for primary partitions (1-4). You can create a partition of any number (1-4) in any order and anywhere on the disk. An extended partition also has an extended MBR for each logical partition (>4) that contains the start location of the next partition which creates a linked list. Removing a logical partition that isn't the last will renumber the list.

The GPT partition table is an array similar to the MBR partition table and has entries for 128 partitions which is the maximum number possible. Also in a similar manner you can create any partition in any numerical order and anywhere on the disk. Some partition tools may not let you pick a partition number. Deleting a partition just deletes that table entry with no affect to any other existing partition.

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Also, from "man gdisk", among the "expert menu" commands:

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So you can renumber misplaced partitions as a separate operation (you can do that on DOS drives too I believe), but they don't get renumbered automatically.

Thanks, guys, that's what I wanted to know.