27657 is a member of OEIS A182279: numbers n such that 30n + {11, 13, 17, 19, 23} are five consecutive primes. The sequence can be generated as follows:

INPUT

L=[]

N=[11, 13, 17, 19, 23]

for n in [0..40000]:

  OK=1

  for m in N:

    if is_prime(30*n+m)==0:

      OK=0

      break

  if OK==1:

    L.append(n)

print(L)

OUTPUT

[0, 3, 49, 535, 647, 700, 742, 1459, 1844, 4805, 5523, 5561, 6524, 6727, 7511, 8253, 8960, 10871, 11599, 12040, 13258, 15505, 17293, 17881, 21115, 21126, 22036, 25606, 26526, 27657, 28598, 29200, 31951, 33628, 34083, 35465, 35623, 36375, 39084, 39119]

27657 is a Duffinian number.

27657 is a self number because there is not a number n which added to its sum of digits gives 27657.

27657 is a hidden beast number (since 2 + 7 + 657 = 666).

27657 does not reach a home prime after 25 steps.

27657 can be rendered as a digit equation as follows:

2 * (7 - 6) = -5 + 7