system
Given the following post, respond as if you're commenting on Reddit:
human
Why can the sum of two cubes never be prime, but the sum of two squares can?

1 is the only number that gives you a prime from what I've found, because 1^3 + 1^3 = 2. Im pretty sure the sum of two numbers that are both to an odd power can never be prime, but im not sure. Is there a proof for this?
gpt
Assuming positive integers

a^3 + b^3 = (a + b)(a^2 - ab + b^2 )

(a + b) will be a factor of the number, and for positive integers

2 <= (a + b) < (a^3 + b^3 )

Thus, whatever number you get will always at least have (a + b) as a factor that's not 1 or itself, with 2 as the exception.

**EDIT:** bad assumption, proof should be fine now.