3 × 7 × 11 × 31 × 331
1, 3, 7, 11, 21, 31, 33, 77, 93, 217, 231, 331, 341, 651, 993, 1023, 2317, 2387, 3641, 6951, 7161, 10261, 10923, 25487, 30783, 71827, 76461, 112871, 215481, 338613, 790097 and 2370291
No.
Its nearest Fibonacci number neighbors are 2178309 and 3524578.