A C150 pilot reported engine failure and diversion to nearby airport.

Narrative

I was flying solo as PIC in my Cessna 150G from ZZZ1 to ZZZ2. Approximately 8 NM south of ZZZ; at 7;500 feet; I began experiencing what I believed was carburetor icing. I applied carb heat; observed a reduction and then a recovery in RPMs. However; the engine roughness persisted after the recovery; which was unusual for this airplane.I made the decision to divert to ZZZ3; located 10 NM west; and canceled flight following with Center. Less than one minute later; the engine failed completely.I configured the airplane for best glide and ran through the emergency checklist. A restart attempt was unsuccessful. I re-established contact with Center; requested priority handling; and turned toward ZZZ; which was now 7.5 NM away.After a second pass through the emergency procedures and still no restart; I focused on making a safe landing. I successfully executed a dead-stick landing at ZZZ without incident.Upon inspection and a call with my A&P; I discovered the primer was loose and not holding pressure; likely causing the engine failure. Notably; I had verified during my in-flight troubleshooting that the primer was in and locked. I reprimed the engine and it restarted without issue. There were 7 gallons of fuel in each tank. I performed a 5-minute static run-up; followed by a 10-minute run-up. After refueling; I safely flew the aircraft back to ZZZ1.The time from initial engine roughness to touchdown was approximately 10 minutes.