I'm guessing the answer to this question is rather large. Skin cells die all the time, it seems, and that never registers as painful. But suppose you rupture or otherwise destroy a group of cells, say in the dermis or something, which enough precision to be able to specify the exact count. How many would you have to destroy before it would be perceptible? What if you add a delay between the destruction of each cell in the group? If it was staggered in time, would that make it imperceptible again?
Although any number estimation would be inaccurate, I can think on two factors that can influence the count.
- Cells location: Pain is trigger when specialize cells (Nociceptors) fires action potentials. The density of those nociceptors is greater in the tip of your finger than in your back. So the number of cell damage that trigger the pain would be different in those areas too.
- Cell death rate: The delay that you mention is a key factor. Slow death like the normal on skin is done by a regulated mechanism (Apoptosis), in this process the cellular components are recycled. In fast cell death, the cellular components are released causing inflammation, which increases the nociceptors sensitivity.