25 × 5 × 13
1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 32, 40, 52, 65, 80, 104, 130, 160, 208, 260, 416, 520, 1040 and 2080
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.