5 × 13 × 71 × 141961
1, 5, 13, 65, 71, 355, 923, 4615, 141961, 709805, 1845493, 9227465, 10079231, 50396155, 131030003 and 655150015
No.
Its nearest Fibonacci number neighbors are 433494437 and 701408733.