Let A = 98765, and B= 4^56788
Then,
98765^4 + 4^56789
= A^4 + 4B^4
= (A^2+2B^2+2AB)(A^2+2B^2-2AB)
Now, A^2+2B^2+2AB = 98765^2+2(4^56788)^2+2*98765*4^56788 98765^2>98765>1
and, (A^2+2B^2-2AB) = (A-B)^2+B^2
= (98765- 4^56788)^2 + (4^56788)^2
> (4^56788^2)^2 >1
Therefore, each of A^2+2B^2+2AB and A^2+2B^2-2AB is >1.
Therefore, A^4+4B^4 is NOT a prime number.
Consequently, the given quantity is NOT a prime number.
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