72 × 29 × 79 × 113
1, 7, 29, 49, 79, 113, 203, 553, 791, 1421, 2291, 3277, 3871, 5537, 8927, 16037, 22939, 62489, 112259, 160573, 258883, 437423, 1812181 and 12685267
No.
Its nearest Fibonacci number neighbors are 9227465 and 14930352.