25 × 3 × 29
1, 2, 3, 4, 6, 8, 12, 16, 24, 29, 32, 48, 58, 87, 96, 116, 174, 232, 348, 464, 696, 928, 1392 and 2784
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.