When was the last common ancestor of pig and human?
Last common ancestor is about 97.5 Million Years Ago.

TimeTree.org Pig vs. Human

That being said, they are close enough to us that they are a vector for influenza viruses that are able to make the jump to human pretty easily.

Also we use their tissue as a homologue for human in forensic research. We also use valves from pig hearts to replace defective human valves.

This Nature News Article reviews some of the work being done with Pig to Human Tissue Transplantation. Though granted the methods they are looking at rely heavily on targeted gene editing.