27349 is a member of OEIS A075282: interprimes which are of the form s*prime, s=7. There are 39 such interprimes in the range up to 40,000. The sequence can be generated as follows (permalink):

INPUT

L,s=[],7

for p in prime_range(40000):

  interprime=(p+next_prime(p))/2

  if interprime%s==0:

    if is_prime(int(interprime/s)):

      L.append(interprime)

print(L)

print(len(L))

OUTPUT

[21, 217, 2191, 2933, 3073, 3353, 7063, 7091, 8813, 9079, 9233, 9527, 9569, 10493, 10717, 11851, 12131, 16667, 17857, 18263, 18347, 19243, 19733, 22421, 23093, 24703, 24787, 25417, 27349, 28637, 32347, 32473, 33607, 33691, 35273, 35413, 36827, 39557, 39613]

39

27349 is an interprime number because it is at equal distance from previous prime (27337) and next prime (27361).

27349 is a Duffinian and lucky number.

27349 is a d-powerful number because it can be written as 2^5 + 7^2 + 3^9 + 4^5 + 9^4.

27349 reaches a stable state under Conway's Game of Life rules after about 140 steps. The stable state consists of one block, two blinkers (period 2), three beehives and another still life (in addition to the block) called a pond. From a "soup" of 49 cells, an "ash" of 36 cells remain.