3 × 11 × 31 × 151 × 331
1, 3, 11, 31, 33, 93, 151, 331, 341, 453, 993, 1023, 1661, 3641, 4681, 4983, 10261, 10923, 14043, 30783, 49981, 51491, 112871, 149943, 154473, 338613, 549791, 1549411, 1649373, 4648233, 17043521 and 51130563
No.
Its nearest Fibonacci number neighbors are 39088169 and 63245986.