As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
DURING CRUISE AT FL410, IN MODERATE TURBULENCE, THE NR 4 ENGINE FLAMED OUT. THE CREW FOLLOWED THE RAPID RESTART PROCEDURE, BUT DID NOT SUCCESSFULLY RESTART THE ENGINE UNTIL REACHING FL310. NO PARAMETERS WERE EXCEEDED AND THE ENGINE OPERATED NORMALLY FOR THE REMAINDER OF THE FLIGHT. MAINTENANCE INSPECTED THE ENGINE PER THE FIM WITH NO DEFECTS NOTED. THE ENGINE WAS RUN AT HIGH POWER WITH ALL INDICATIONS NORMAL.