27733 is a 4k+1 prime and thus it can be expressed as a sum of two squares in one way only viz. 142^2 + 87^2.

27733 is the first prime in a series of six primes such that the gap between first and last is 18. See blog post Density of Primes. The initial numbers with this property are:

11, 13, 29, 223, 1289, 1481, 1861, 4783, 5639, 5641, 13679, 27733, 44263, 80669, 88799, 88801, 93479

It is also the FIRST term in a sequence of primes with the pattern 4, 2, 4, 6, 2. Thus we have the chain of primes 27733, 27737, 27739, 27743, 27749, 27751. See blog post from 8th March 2025 titled Density of Primes. In the range up to 40000, this pattern only occurs for starting primes 13, 223, 4783 and 27733 (permalink).

27733 is a nialpdrome in base 6 : 332221.

27733 is a good prime. See Numbers Aplenty link.

27733 can be rendered as a digit equation as follows:

2 = 7 / 7 + 3 / 3