27381 is a member of OEIS A034818: concatenations p1, p2, p3 are all prime where (using | to represent concatenation) we have:

p1 = next_prime(n) | n

p2 = n | previous_prime(n)

p3= next_prime(n) | n | previous_prime(n)

p1 = 2739727381

p2 = 2738127367

p3 = 273972738127367

The sequence can be generated using the following algorithm (permalink):

INPUT

L=[]

for n in [3..40000]:

  p1=int(str(next_prime(n))+str(n))

  p2=int(str(n)+str(previous_prime(n)))

  p3=int(str(next_prime(n))+str(n)+str(previous_prime(n)))

  if n==27381:

    print(p1,p2,p3)

  if is_prime(p1)==1 and (is_prime(p2)==1 and is_prime(p3)==1):

      L.append(n)

print()

print(L)

OUTPUT

2739727381 2738127367 273972738127367

[657, 4929, 10647, 18291, 20907, 22653, 27381, 28053, 28671]

27381 is a Duffinian, congruent and D-number.

27381 is a balanced number in the sense that 2 + 7 = 9 and 8 + 1 = 9.

27381 can be rendered as a digit equation thus:

2 = (7 + 3) // 8 + 1.

27381 stabilises after about 30 generations to a single traffic light and a single glider.