27449 is a 4k+1 prime and can therefore be expressed as a sum of two squares in one way only viz. 160^2 + 43^2.

27449 is a member of OEIS A029949: smallest prime containing n-th cube as substring, here n=14 and n^3=2744. The sequence can be generated as follows:

INPUT

L=[]

C=[n^3 for n in [0..17]]

for c in C:

  for p in prime_range(1000000):

    if str(c) in str(p):

      L.append(p)

      break

print(L)

OUTPUT

[101, 11, 83, 127, 641, 1259, 2161, 3343, 15121, 2729, 10007, 13313, 117281, 12197, 27449, 33751, 40961, 34913]

27449 is a de Polignac number because none of the positive numbers 27449 - 2^k is a prime.

27449 can be rendered as a digit equation as follows:

2 + 7 + 4 - 4 = 9

27449 stabilises after about 570 generations of Conway's Game of Life to four gliders and an assortment of still life shapes and oscillators.