32 × 11 × 31 × 151
1, 3, 9, 11, 31, 33, 93, 99, 151, 279, 341, 453, 1023, 1359, 1661, 3069, 4681, 4983, 14043, 14949, 42129, 51491, 154473 and 463419
No.
Its nearest Fibonacci number neighbors are 317811 and 514229.