Primal Red, like any other of the Primal Blocks, can be gathered by mining the ground, trees and structures, rocks and mountains and so forth. Everything that is not a special mine block converts to a primal one.
For the farming purposes of Primal Red, it is highly recommended to head on to the desert biome. The very top layer of the desert is covered with blocks that grant you a piece of red. It's fast, it's easy and can be used to make some red carpet to your all mighty hallway.