7 × 11 × 43 × 89 × 401
1, 7, 11, 43, 77, 89, 301, 401, 473, 623, 979, 2807, 3311, 3827, 4411, 6853, 17243, 26789, 30877, 35689, 42097, 120701, 189673, 249823, 294679, 392579, 1327711, 1534627, 2748053, 10742389, 16880897 and 118166279
No.
Its nearest Fibonacci number neighbors are 102334155 and 165580141.