3 × 89 × 277 × 39983
1, 3, 89, 267, 277, 831, 24653, 39983, 73959, 119949, 3558487, 10675461, 11075291, 33225873, 985700899 and 2957102697
No.
Its nearest Fibonacci number neighbors are 1836311903 and 2971215073.