52 × 11 × 101 × 151
1, 5, 11, 25, 55, 101, 151, 275, 505, 755, 1111, 1661, 2525, 3775, 5555, 8305, 15251, 27775, 41525, 76255, 167761, 381275, 838805 and 4194025
No.
Its nearest Fibonacci number neighbors are 3524578 and 5702887.