7 × 23 × 89 × 599479
1, 7, 23, 89, 161, 623, 2047, 14329, 599479, 4196353, 13788017, 53353631, 96516119, 373475417, 1227133513 and 8589934591
No.
Its nearest Fibonacci number neighbors are 7778742049 and 12586269025.