27665 is a number n such that n plus digit sum of n and n-1 plus digit sum of n-1 are both prime, here 27665 + 26 = 27691 (prime) and 27664 + 25 = 27689 (prime).

Here are the remaining such numbers:

27665, 27716, 27731, 27887, 27917, 28076, 28091, 28163, 28256, 28328, 28385, 28526, 28547, 28589, 28637, 28727, 28988, 29006, 29114, 29375, 29645, 29735, 29849, 29978, 30005, 30131, 30374, 30449, 30539, 30824, 30848, 31109, 31142, 31166, 31235, 31298, 31307, 31493, 31502, 31526, 31697, 31706, 31709, 31748, 31832, 32021, 32045, 32111, 32132, 32174, 32282, 32312, 32354, 32393, 32402, 32426, 32516, 32591, 32777, 32885, 32918, 32951, 33056, 33164, 33272, 33329, 33566, 33581, 33728, 33746, 33785, 33812, 34022, 34115, 34139, 34193, 34202, 34244, 34283, 34352, 34448, 34481, 34487, 34571, 34628, 34736, 34823, 34826, 34937, 35036, 35258, 35300, 35432, 35567, 35699, 35708, 35816, 35873, 35984, 36002, 36086, 36446, 36512, 36755, 36869, 36911, 36992, 37181, 37322, 37343, 37526, 37547, 37565, 37784, 37964, 38222, 38312, 38426, 38441, 38579, 38627, 38645, 38684, 38888, 39143, 39212, 39218, 39323, 39347, 39479, 39815]

27665 is a sphenic, Duffinian and Curzon number.

27665 can be rendered as a digit equation as follows:

-2 + 7 = 6 - 6 + 5