27427 is a member of OEIS A296563: Yarborough primes that remain Yarborough primes when each of their digits are replaced by their cubes, here 8343648343. See blog post Yarborough and Anti-Yarborough Primes. The sequence can be generated as follows (permalink):

INPUT

L=[]

for p in prime_range(40000):

  if "0" not in str(p) and "1" not in str(p):

    number=""

    for d in str(p):

      number+=str(int(d)^3)

    if is_prime(int(number)):

      if "0" not in number and "1" not in number:

        L.append(p)

        if p == 27427:

          print(p,"-->",int(number))

print(L)

OUTPUT

27427 --> 8343648343

[23, 43, 73, 229, 233, 277, 449, 773, 937, 947, 2239, 2243, 2297, 2377, 2777, 3299, 3449, 3727, 3943, 4243, 4423, 4493, 7393, 7723, 7927, 7949, 9227, 9743, 9749, 22277, 22727, 22777, 22943, 23327, 23399, 23497, 23747, 24473, 24733, 27239, 27277, 27427, 27799, 29347, 29443, 29723, 32443, 33247, 33343, 34729, 37223, 39727, 39749, 39779, 39937]

27427 is a lucky number.

27427 is a junction number because it is equal to n+sod(n) for n = 27398 and 27407.

27427 can be converted to a digit equation as follows:

-2 + 7 + 4 = 2 + 7

27427 stabilises after about 750 generations of Conway's Game of Life to an assortment of blinkers and still life shapes.