74 × 11 × 73
1, 7, 11, 49, 73, 77, 343, 511, 539, 803, 2401, 3577, 3773, 5621, 25039, 26411, 39347, 175273, 275429 and 1928003
No.
Its nearest Fibonacci number neighbors are 1346269 and 2178309.