32 × 31 × 37 × 41
1, 3, 9, 31, 37, 41, 93, 111, 123, 279, 333, 369, 1147, 1271, 1517, 3441, 3813, 4551, 10323, 11439, 13653, 47027, 141081 and 423243
No.
Its nearest Fibonacci number neighbors are 317811 and 514229.