2 × 3 × 5 × 7 × 17
1, 2, 3, 5, 6, 7, 10, 14, 15, 17, 21, 30, 34, 35, 42, 51, 70, 85, 102, 105, 119, 170, 210, 238, 255, 357, 510, 595, 714, 1190, 1785 and 3570
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.