5 × 7 × 11 × 17 × 23
1, 5, 7, 11, 17, 23, 35, 55, 77, 85, 115, 119, 161, 187, 253, 385, 391, 595, 805, 935, 1265, 1309, 1771, 1955, 2737, 4301, 6545, 8855, 13685, 21505, 30107 and 150535
No.
Its nearest Fibonacci number neighbors are 121393 and 196418.