7 × 11 × 73 × 101 × 137
1, 7, 11, 73, 77, 101, 137, 511, 707, 803, 959, 1111, 1507, 5621, 7373, 7777, 10001, 10549, 13837, 51611, 70007, 81103, 96859, 110011, 152207, 567721, 770077, 1010101, 1065449, 7070707, 11111111 and 77777777
No.
Its nearest Fibonacci number neighbors are 63245986 and 102334155.