22 × 3 × 5 × 37
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 37, 60, 74, 111, 148, 185, 222, 370, 444, 555, 740, 1110 and 2220
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.