11 × 41 × 271 × 9091
1, 11, 41, 271, 451, 2981, 9091, 11111, 100001, 122221, 372731, 2463661, 4100041, 27100271, 101010101 and 1111111111
No.
Its nearest Fibonacci number neighbors are 701408733 and 1134903170.