25 × 7 × 11
1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 32, 44, 56, 77, 88, 112, 154, 176, 224, 308, 352, 616, 1232 and 2464
No.
Its nearest Fibonacci number neighbors are 1597 and 2584.