27484 is a number that is the larger of a pair of adjacent composite numbers such that both are only one step away from their home primes. Here 27483 = 3 * 9161 --> 39161 is prime and 27484 = 2^2 * 6871 --> 226871 is also prime. See Bespoken for Sequences entry.

27484 is an interprime number because it is at equal distance from previous prime (27481) and next prime (27487).

27484 is a concatenation of 3^3 and 22^2. Concatenations of this general sort are fairly rare in the range up to 40000 where we only have (permalink) 44, 274, 427, 2564, 2727, 4256, 4484, 4844, 25627, 27256, 27484 and 31254 with concatenated parts shown below:

44 = 2^2 || 2^2

274 = 3^3 || 2^2

427 = 2^2 || 3^3

2564 = 5^2 || 4^3 or 4^3 | | 2^2

2727 = 3^3 || 3^3

4256 = 2^2 || 4^4

4484 = 2^2 || 22^2

25627 = 4^4 || 3^3

27256 = 3^3 || |4^4

27284 = 3^3 || 22^2

31254 = 5^5 || 2^2

The criterion is that BOTH concatenated numbers must have the same BASE and INDEX digits. Even though in the examples above all indices are one digit long, we could have numbers like 2^22 || 3^33 and so on. These of course are very large numbers but they still satisfy the criterion but are outside of our range of interest.

27484 can be rendered as a digit equation as follows:

( 2^7 / 4 ) / 8 = 4