2 × 3 × 5 × 7 × 11
1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155 and 2310
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.