27351 is a member of OEIS A181619: numbers k such that k^2+1 = 2*p,(k+1)^2+1 = 5*q, (k+2)^2+1 = 10*r where p, q, and r are primes. The sequence can be generated as follows (permalink):

INPUT

L=[]

for n in [1..40000]:

  p=(n^2+1)/2

  if int(p)==p:

    if is_prime(int(p)):

      q=((n+1)^2+1)/5

      if int(q)==q:

        if is_prime(int(q)):

          r=((n+2)^2+1)/10

          if int(r)==r:

            if is_prime(int(r)):

              L.append(n)

print(L)

OUTPUT

[11, 51, 61, 101, 221, 261, 571, 2271, 2821, 2871, 5071, 5651, 5761, 6561, 6951, 9751, 10461, 10851, 11621, 11711, 14961, 15911, 16551, 17171, 17601, 18511, 19071, 19551, 23151, 25261, 27351, 27751, 30421, 32801, 37051, 38651, 38801, 38911]

27351 after about 190 steps stabilises to six blocks, one ship, one blinker and two gliders.