27479 is a member of OEIS A059763: primes starting a Cunningham chain of the first kind of length 4. The progression is 27479 --> 54959 --> 109919 --> 219839. All members are "unsafe" primes and all chains are exactly of length 4 and no larger.

The following algorithm will generate the initial members of the sequence (permalink):

INPUT

L=[]

for p in prime_range(2,40000):

  if is_prime(int((p-1)/2))==0:

    if is_prime(2*p+1) and is_prime(4*p+3):

      if is_prime(8*p+7) and is_prime(16*p+15)==0:

        L.append(p)

print(L)

print()

p=27479

print(p,"-->",2*p+1,"-->",4*p+3,"-->",8*p+7)

OUTPUT

[509, 1229, 1409, 2699, 3539, 6449, 10589, 11549, 11909, 12119, 17159, 19709, 19889, 22349, 26189, 27479, 30389]

27479 --> 54959 --> 109919 --> 219839

27479 is a Sophie Germain prime and twin prime with 27481.

27479 is a de Polignac number because none of the positive numbers 27479-2^k is a prime.

27479 is a d-powerful number because it can be written as 2^3 + 7 + 4^6 + 7^5 + 9^4.

27479 can be written as a digit equation as follows:

2 | (7 + 4 + 7) = 9