5 × 41 × 271 × 9091
1, 5, 41, 205, 271, 1355, 9091, 11111, 45455, 55555, 372731, 1863655, 2463661, 12318305, 101010101 and 505050505
No.
Its nearest Fibonacci number neighbors are 433494437 and 701408733.