7 × 11 × 13 × 37 × 101
1, 7, 11, 13, 37, 77, 91, 101, 143, 259, 407, 481, 707, 1001, 1111, 1313, 2849, 3367, 3737, 5291, 7777, 9191, 14443, 26159, 37037, 41107, 48581, 101101, 287749, 340067, 534391 and 3740737
No.
Its nearest Fibonacci number neighbors are 3524578 and 5702887.