27697 is a 4k+1 prime and can therefore be expressed as a sum of two squares in one way only viz. 111^2+124^2.
27697 is a member of OEIS A160440: smaller member of a pair (p,q) of cousin primes such that p and q are in different centuries (here q = 27701). The sequence can be generated as follows:
INPUT
L=[]
for n in [1..400]:
if is_prime(100*n-1) and is_prime(100*n+3):
L.append(100*n-1)
if is_prime(100*n-3) and is_prime(100*n+1):
L.append(100*n-3)
print(L)
OUTPUT
[97, 397, 499, 1297, 1597, 1999, 2797, 3697, 4999, 6199, 6997, 7699, 9199, 10099, 10597, 12097, 13099, 16699, 18397, 20899, 21397, 21499, 21799, 23197, 23599, 25999, 26497, 27697, 27799, 27997, 32299, 32797, 33199, 34297, 35797, 38197, 38299, 39499]
27697 is a member of OEIS A086424: numbers needed to generate all other natural numbers, only allowing multiplication and addition. Each number can be used only once. See blog post Building Block Numbers.
27697 is a happy number.
27697 is a d-powerful number since 27697 = 2^13 + 7^4 + 6^3 + 9^2 + 7^5.
27697 is a palindrome in base 12 = 14041
27697 can be rendered as a digit equation as follows:
-2 * (7 - 6) + 9 = 7