Craftsman 3.5 edger starts when primed, but will not stay running. If I keep pushing the primar it will run until I stop pushing it. Could this be a fuel filter problem or due to old gasoline? Help!

Dump out the fuel and start with a fresh tank just to eliminate that as an issue. This sounds like the carb is already getting clogged so add a dash of SeaFoam or other carb cleaner to the first tank.