A072752,A001348,A100105

[N. J. A. Sloane]

Primes of the form semiprime(a)^semiprime(a) + semiprime(b)^semiprime(b).

Primes of the form A114850(a) + A114850(b).

a(1) = 437893890380859631 = 256 + 437893890380859375 = 4^4 + 15^15 =
semiprime(1)^semiprime(1) + semiprime(6)^semiprime(6).

a(2) = 88817841970012523233890533447265881 = 256 +
88817841970012523233890533447265625 = 4^4 + 25^25 =
semiprime(1)^semiprime(1) + semiprime(9)^semiprime(9).

a(3) =  46656 + 88817841970012523233890533447265625 = 6^6 + 24^25 =
semiprime(2)^semiprime(2) + semiprime(9)^semiprime(9).

Comment: This is to A068145 Primes of the form a^a + b^b as A001358
semiprimes is to A000040 primes; and as A114850 (n-th semiprime)^(n-th
semiprime) is to A051674 (n-th prime)^(n-th prime).

Is this right so far?  Would someone like to extend?

cf. A000040, A001358, A051674, A068145, A114850.