27393 is a member of OEIS A034817: concatenations where 'prevprime(n) + n', 'n + nextprime(n)' and 'prevprime(n) + n + nextprime(n)' are all prime. Here the primes are:

2736727393

2739327397

273672739327397

The sequence can be generated as follows (permalink):

INPUT

L=[]

for n in [3..40000]:

  a=int(str(previous_prime(n))+str(n))

  b=int(str(n)+str(next_prime(n)))

  c=int(str(previous_prime(n))+str(n)+str(next_prime(n)))

  if is_prime(a) and (is_prime(b) and is_prime(c)):

    L.append(n)

if n==27393:

       print(a,b,c)

print(L)

OUTPUT

2736727393 2739327397 273672739327397

[63, 333, 621, 3339, 4557, 8127, 13977, 16827, 18177, 21921, 27393, 34989]

Compare this sequence to that of OEIS A034818.

27393 has three distinct prime factors each of which contains the digit 3. There are 240 such numbers in the range up to 40000. From 27393 to 40000, these numbers are (permalink):

[27393, 27507, 28137, 28551, 28587, 28689, 28767, 28821, 28923, 28977, 29109, 29193, 29419, 29481, 29627, 29739, 29877, 30003, 30057, 30147, 30291, 30441, 30567, 30659, 30687, 30783, 30797, 30831, 31341, 31413, 31947, 32097, 32271, 32457, 32523, 32619, 32721, 32829, 33267, 33387, 33449, 33657, 33787, 33927, 34077, 34113, 34131, 34437, 34521, 34611, 34689, 34707, 34743, 34917, 35113, 35187, 35247, 35457, 35619, 35697, 36087, 36177, 36507, 36543, 36593, 36741, 36921, 37047, 37167, 37407, 37789, 37797, 37887, 38001, 38337, 38517, 38739, 38847, 39169, 39183, 39507, 39603, 39849, 39923]

27393 is a sphenic, Curzon and lucky number.

27393 is a Proth number since it is equal to 107 ⋅ 2^8 + 1 and 107 < 2^8.

27393 can be written as a digit equation in the following way:

2 + 7 = 3 + 9 - 3

27393 stabilises after a little more than 900 generations of Conway's Game of Life to an assorted of still lifes (blocks, beehives, honey farms, ships) and oscillating traffic lights and blinkers. No gliders were generated.