<s>[INST] Prove that $2^{10}+5^{12}$ is composite 
Prove that $2^{10}+5^{12}$ is composite

I need to solve this using only high school mathematics.
Any ideas?
 [/INST] $$2^{10} + 5^{12} = (5^3)^4 + 4(2^2)^4 = 125^4 + 4\cdot4^4$$
And then the result follows from Sophie Germain's identity, ie, $$a^4 + 4b^4 = (a^2 + 2ab + 2b^2)(a^2 - 2ab + 2b^2)$$
Yielding, $$2^{10} + 5^{12} = (5^6 + 10^3 + 2^5)(5^6 - 10^3 + 2^5) = 16657\cdot 14657$$
</s>