Showerthought: I ran a 4-wire alarm cable next to a power line for 20 feet and got constant false trips

I was finishing a basement job in Springfield and had to get a sensor run across the ceiling. The path went right alongside the main 120V line feeding the room, about two inches apart. For three days the system kept triggering the motion detector as a fault. I finally put a meter on the line and saw interference spikes every time the furnace kicked on. Learned my lesson about parallel runs with AC power, even for short distances. What's the minimum separation you guys keep for low voltage next to house wiring?