DURING A CRUISE CLIMB, THE AIRCREW NOTED AN UNUSUAL VIBRATION; HOWEVER, ATTEMPTS TO ISOLATE THE VIBRATION WERE UNSUCCESSFUL. WHILE CLIMBING FROM FL190 TO FL250, THE FLT ENGINEER WENT AFT TO OBSERVE THE ENGS & PROPS, BUT NOTED NOTHING UNUSUAL. A FLT ATTENDANT WENT FORWARD TO ADVISE THE CAPT THAT NOTHING WAS OBSERVED, WHEN THE VIBRATION INCREASED IN INTENSITY. AS SHE LEFT THE COCKPIT, SHE PEERED OUT THE RGT WINDOW & SAW THE #4 PROP SEPARATE & STRIKE THE ACFT. THIS CAUSED MAJOR DAMAGE TO THE LOWER FUSELAGE & RESULTED IN DECOMPRESSION OF THE CABIN. THE FLT CONTROLS BECAME JAMMED & THE ENGS WOULD NOT RESPOND TO THROTTLE MOVEMENT. THE AUTOPLT WAS USED FOR MINIMAL CONTROL & THE FLT CREW WERE ABLE TO DIVERT TO ANCHORAGE, AK. THEY WERE ABLE TO CLIMB & DESCEND BY RETRACTING & EXTENDING THE LANDING GEAR WITH THE #2 ENG SHUT DOWN. THE ACFT WAS LANDED SAFETY & THE ENGS WERE SHUT DOWN TO DECELERATE . THE EXACT CAUSE OF THE PROP SEPARATION WAS NOT DETERMINED SINCE IT FELL IN THE OCEAN DURING THE OCCURRENCE.