27617 is a 4k+1 prime and can thus be expressed as a sum of two squares in one way only viz. 119^2 + 116^2.

27617 is a member of OEIS A131748: minimum prime that raised to the powers from 1 to n produces numbers whose sums of digits are also primes, here n=7. See blog post A Prime to Remember.

27617 is a member of OEIS A176179: primes such that the sum of digits, the sum of the squares of digits and the sum of 3rd powers of their digits is also a prime.

Here are the 73 primes from 27617 up to 40000 that satisfy the criteria:

[27617, 27749, 27947, 28111, 28351, 28513, 28559, 29989, 30011, 30307, 30323, 30347, 30367, 30491, 30637, 30703, 30763, 30853, 30941, 31247, 31333, 31393, 31847, 31991, 32141, 32303, 32411, 32969, 33023, 33113, 33203, 33311, 33331, 33353, 33391, 33533, 33863, 33931, 34019, 34127, 34141, 34211, 34217, 34439, 34703, 34721, 34781, 34871, 35069, 35083, 35281, 35803, 36037, 36073, 36161, 36299, 36307, 36383, 36389, 36697, 36833, 36929, 37003, 38053, 38639, 38693, 39041, 39119, 39133, 39191, 39313, 39443, 39667, 39863]

27617 is a happy number.

27617 is an inconsummate number since there does not exist a number n which divided by its sum of digits gives 27617.

27617 is a junction number because it is equal to n+sod(n) for n = 27592 and 27601.

27617 is a d-powerful (and thus energetic) number because it can be written as 2^13 + 7^4 + 6^3 + 1 + 7^5.

27617 is a nialpdrome in base 13 (c755) because all the digits are non-increasing.

27617 can be rendered as a digit equation as follows:

-2 + 7 = 6 - 1 ^ 7