27311 is a member of OEIS A178328: numbers k such that k^p-p is prime, where p is product of the digits of k. These primes are very large and the algorithm designed to generate the initial members of the sequence quickly stalls. Here are the initial members:

2, 21, 121, 211, 223, 631, 1211, 1663, 1811, 1831, 2127, 2813, 4211, 5497, 6211, 8411, 12149, 12287, 18113, 19121, 23311, 24113, 24311, 27311, 31651, 32129, 32221, 34171, 38131, 41213, 47231, 49183, 53831, 56831, 111223, 111421, 111811, 121279, 123121, 129151, 141233, 156271, 157651, 161171

27311 is a cyclic and Duffinian number.

27311 is a de Polignac number because none of the positive numbers 27311 -2^k is a prime.