25 × 7 × 23
1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 56, 92, 112, 161, 184, 224, 322, 368, 644, 736, 1288, 2576 and 5152
No.
Its nearest Fibonacci number neighbors are 4181 and 6765.