22 × 3 × 7 × 31
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 31, 42, 62, 84, 93, 124, 186, 217, 372, 434, 651, 868, 1302 and 2604
No.
Its nearest Fibonacci number neighbors are 2584 and 4181.