25 × 11 × 31
1, 2, 4, 8, 11, 16, 22, 31, 32, 44, 62, 88, 124, 176, 248, 341, 352, 496, 682, 992, 1364, 2728, 5456 and 10912
No.
Its nearest Fibonacci number neighbors are 6765 and 10946.