27583 is a member of OEIS A296187: Yarborough primes that remain Yarborough primes when each of their digits are replaced by their squares, here 44925641. See blog post titled Yarborough and Anti-Yarborough Primes.

The sequence can be generated as follows:

INPUT

L=[]

for p in prime_range(40000):

  D=p.digits()

  if 0 not in D and 1 not in D:

    number=""

    for d in str(p):

      number+=str(int(d)^2)

    if is_prime(int(number))and("0" not in number and "1" not in number):

      L.append(p)

print(L) 

OUTPUT

[73, 223, 233, 283, 337, 383, 523, 733, 773, 823, 2333, 2683, 2833, 2857, 3323, 3583, 3673, 3733, 3853, 5333, 6673, 6737, 6883, 7333, 7673, 7727, 7877, 8233, 8563, 8623, 22277, 22283, 22727, 23333, 23833, 25237, 25253, 25633, 26227, 26833, 27583, 27827, 27883, 32257, 32323, 32633, 33863, 35227, 35323, 35527, 35533, 35863, 36383, 36683]

27583 is a plaindrome in base 16 (6bbf).

27583 is a member of OEIS A124595: primes p such that q-p = 28, where q is the next prime after p.

Initial members are:

2971, 3271, 5119, 5953, 8971, 10009, 10399, 10531, 10909, 11551, 13339, 14563, 14593, 16273, 16843, 18013, 18919, 21031, 21529, 23371, 23929, 24631, 27211, 27583, 28123, 29761, 32803, 34183, 37663, 38011, 39631, 39901

27583 is a member of OEIS A091368: primes p such that the sum of the digits of p is not prime, but the sum of each digit raised to the 4th power is prime.

The initial members are:

1699, 2689, 6199, 6829, 6991, 7477, 8089, 8269, 8629, 9619, 12589, 15289, 19069, 19609, 20599, 20959, 21589, 21859, 23857, 25189, 25819, 25873, 25981, 27259, 27529, 27583, 28069, 28537, 28573, 28591, 28753, 29059, 29527, 29581, 29851

OEIS comment:

Apparently, for primes such that each digit raised to the 4th power sum to a prime, it is more likely that the digits themselves also sum to a prime. In the first 10,000 primes there are 760 primes whose digits raised to the 4th power sum to a prime. Of these, only 106 are such that the sums of the digits are not prime. Interestingly, all of these primes have a digit sum of 25 or 35. Essentially this sequence is the terms of A091367 (primes whose digits raised to the 4th power sum to a prime) that do not also appear in A046704 (primes whose digits sum to a prime).

27583 can be rendered as a digit equation as follows:

2 + 7 = (-5 + 8) * 3