GROSS NAV ERROR. FLC DEV OCCURS IN AN OVERWATER NIGHT OP. POTENTIAL CONFLICT LTSS.

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ATC FACILITY: SHANNON. LOCATION: 75 NM W OF 5115N. UPON RECEIVING DATA LINK CLRNC BEFORE COAST-OUT AT BANCS; THE CREW DETERMINED THAT THE ONLY CHANGE TO THE ORIGINAL FLT PLAN WAS THE REPLACEMENT OF POS GIPER WITH POS KENUK AND CHANGED THE FMC ACCORDINGLY. BECAUSE OF THE SIMILAR APPEARANCE OF 5015N AND 5115N; THE CHANGE FROM 5115N TO 5015N WAS OVERLOOKED. AT XX50Z AND APPROX 75 NM W OF 5115N; THE CREW NOTED AN ACFT ON TCASII AT THE SAME ALT OFF THE L WING AT A RANGE OF 15 MI. THE CREW IMMEDIATELY STARTED TO CHK THE CURRENT POS AND THE NEXT POS. THE PNF SWITCHED TO SHANNON ON VHF TO INQUIRE ABOUT THE PROX OF THE OTHER ACFT. AS SOON AS VHF WAS SELECTED; THE CREW WAS CONTACTED BY SHANNON AND GIVEN A SQUAWK THAT WAS FOLLOWED IMMEDIATELY BY A DIRECTED 30 DEG TURN TO THE R. SOON THEREAFTER; SHANNON INFORMED THE CREW THAT IT WAS EXPECTED AT 5015N AND NOT 5115N. AFTER RECHKING THE FMC VERSUS THE FLT PLAN VERSUS THE DATA LINK CLRNC; THE CREW DETERMINED THAT THE CLRNC HAD; IN FACT; INCLUDED THE CHANGE 5015N; KENUK. IT HAD 5115N; KENUK IN THE FMC. CAPT'S OBSERVATIONS; IN RETROSPECT; WE CONTINUOUSLY REFERRED TO 5115N AS 5015N AND WERE MENTALLY LOCKED ONTO THE FACT THAT KENUK WAS THE ONLY CHANGE TO OUR FLT PLAN. OBVIOUSLY; WE ARE ALL VERY UPSET THAT THIS ERROR OCCURRED AND HAVE DISCUSSED AT LENGTH BTWN OURSELVES HOW TO PREVENT THIS FROM HAPPENING AGAIN. SUPPLEMENTAL INFO FROM ACN 356630: WE FEEL THAT USING THE ACTUAL DATA LINK CLRNC AS A FINAL CHK AGAINST THE WAYPOINTS ENTERED INTO THE FMS PRIOR TO COASTOUT WOULD PREVENT ANY POSSIBLE IMPROPER XFER OF DATA.