25 × 5 × 7
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 70, 80, 112, 140, 160, 224, 280, 560 and 1120
No.
Its nearest Fibonacci number neighbors are 987 and 1597.