22 × 3 × 13 × 71
1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 71, 78, 142, 156, 213, 284, 426, 852, 923, 1846, 2769, 3692, 5538 and 11076
No.
Its nearest Fibonacci number neighbors are 10946 and 17711.