# Prime-cubes can be good too!

Call a positive integer $$N$$ $$\textbf{good}$$, if it is prime and the cube of the number in decimal representation can be split into 3 parts such that their sum adds up to the original number.

Let $$N_1, N_2, N_3, ..., N_n$$ be all of the distinct $$\textbf{good}$$ numbers on the interval $$[1, 10^9]$$. Determine the value of $$R$$ if:

$\sum^{n}_{i=1}N_{i}^{N_{i}}\equiv R \mod10^{10}$

Details and Test cases:

• $$0$$ is not a positive integer.
• Consider $$297^3= 26198073$$. So, $$26+198+73 = 297$$. But it is not a good number since $$297$$ is not prime.
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