27509 is a 4k+1 prime and so it can be expressed as a sum of two squares in one way only viz. 130^2 + 103^2.

27509 is a member of OEIS A023317: primes that remain prime through 4 iterations of function f(x) = 6x + 5. The sequence is generated as follows (permalink):

INPUT

L=[]

for p in prime_range(40000):

  number=p

  OK=1

  for i in [1..4]:

    p=6*p+5

    if is_prime(p)==0:

      OK=0

      break

  if OK==1:

    L.append(number)

print(L)

OUTPUT

[11, 13, 83, 151, 317, 373, 1721, 3529, 4153, 4243, 4637, 4783, 5209, 5849, 5923, 6661, 8431, 10903, 11329, 14519, 16183, 16979, 20149, 26669, 27509, 27827, 29873, 29947, 32987, 33637, 33937, 34919, 35099, 35543, 36277, 36691, 38069, 38461]

Of these numbers, a few will survive another iteration and these are 13, 4637, 5849, 5923, 16183, 16979, 34919 and 36277. None survive six iterations within the range up to 40,000. However, if we extend the range to one million, there are three numbers that survive and these are 15571, 249133 and 972197. None survive seven iterations.

27509 can be rendered as a digit equation as follows:

-2 + 7 - 5 = 0 * 9