27409 is a 4k+1 prime and thus it can be expressed as a sum of two squares in one way only viz. 28^2 + 105^2.

27409 is a member of OEIS A228529: a(n) = prime(n*prime(n)). The sequence can be generated as follows:

INPUT

L=[]

for n in [1..35]:

  number=nth_prime(n*nth_prime(n))

  L.append(number)

print(L)

OUTPUT

[3, 13, 47, 107, 257, 397, 653, 881, 1279, 1889, 2293, 3119, 3847, 4423, 5323, 6563, 7937, 8819, 10391, 11833, 12889, 14831, 16477, 18713, 21599, 23603, 25189, 27409, 29063, 31511, 37159, 39869, 43321, 45589, 50923]

27409 is a lucky and self number.

27409 can be converted to a digit equation as follows:

2 + 7 + 4 * 0 = 9

27409 stabilises after about 300 generations of Conway's Game of Life to two gliders, a single oscillator and an assortment of still life shapes.