2 × 3 × 5 × 13 × 29
1, 2, 3, 5, 6, 10, 13, 15, 26, 29, 30, 39, 58, 65, 78, 87, 130, 145, 174, 195, 290, 377, 390, 435, 754, 870, 1131, 1885, 2262, 3770, 5655 and 11310
No.
Its nearest Fibonacci number neighbors are 10946 and 17711.