27418 is a product of 2 and a 4k+1 prime and so it can be expressed as a sum of two squares in one way only viz. 137^2 + 93^2.

27418 is an interprime number that is also a semiprime with both factors having the same digital root, here 2. There are 78 such numbers in the range up to 40000. This algorithm will generated them:

INPUT

L=[]

for p in prime_range(40000):

  number=(p+next_prime(p))/2

  if len(prime_factors(number))==2 and len(divisors(number))==4:

    P=prime_factors(number)

    b=10

    if sum(P[0].digits(b))%(b-1)!=0:

      dr1=sum(P[0].digits())%(b-1)

    else:

      dr1=9

    if sum(P[1].digits(b))%(b-1)!=0:

      dr2=sum(P[1].digits())%(b-1)

    else:

      dr2=9

    if dr1==dr2:

      L.append(number)

print(L)

print(len(L))

OUTPUT

[205, 274, 1207, 1465, 2191, 3073, 3265, 3694, 4054, 4594, 4846, 4954, 5833, 5854, 6667, 7402, 7597, 7957, 7978, 8014, 8266, 9193, 9346, 9637, 9655, 10363, 10645, 11293, 12085, 12514, 12847, 13303, 14998, 15613, 16045, 16753, 16837, 17503, 18295, 18454, 18649, 19519, 19606, 20095, 20527, 20578, 20737, 21667, 22297, 22558, 23239, 23587, 24127, 24721, 24883, 26734, 26827, 27037, 27247, 27382, 27418, 28915, 29089, 30823, 31057, 32197, 33043, 33217, 33691, 34135, 34477, 35806, 37822, 38293, 38581, 38758, 39613, 39691]

78

27418 is a balanced number in that 2 + 7 = 1 + 8 = 9 around the central 4 which is also the arithmetic digital root of the number.

27418 is a Smith number since the sum of its digits (22) coincides with the sum of the digits of its prime factors. Since it is squarefree, it is also a hoax number.

27418 can be written as a digit equation as follows:

-2 + 7 - 4 = 1 ^ 8

27418 stabilises after about 45 generations of Conway's Game Life to two still life blocks. It can be noted that 27417 produced a similar outcome but with four still life blocks.