WASHINGTON — Cast members, producers, hundreds of sailors and even a few Coasties gathered here Wednesday night to attend the premiere of “The Last Ship,” a TV show in which the crew of the fictional destroyer Nathan James attempts to save the world from a deadly virus. The stars walked the blue carpet at the Newseum in downtown Washington, D.C., while sailors mingled at a reception in the lobby to music from a Navy band to celebrate the opening of a drama where the U.S. Navy is the world’s last, best hope. The Navy’s Office of Information-West played a key…