Factorizing sum of two powers.

Question

Is it possible to factorize, I'm trying to prove it isn't prime.

$x^4 + 15^x$

If for what values of x will the above be prime, also any general method of determining if a really large number is prime?

Thanks.

I'm not sure if it can be factorised, but note that $2^4 + 15^2 = 241$ is a prime. As others have pointed out, if $x$ is odd, then so are $x^4$ and $15^x$ and hence their sum is even. — JavaMan, Dec 11 '12 at 08:58

score 1 · Accepted Answer · answered Dec 11 '12 at 08:12

1

Definitely not a prime-- any odd value of x spoiling it.

answered Dec 11 '12 at 08:12

ashley

1,023

score 0 · Answer 2 · answered Dec 11 '12 at 08:24

As user 'ashley' has pointed, any odd number would damage it. To check the primality in general, there is a deterministic polynomial time algorithm. Please refer the famous paper which proves constructively to check if a number is prime or not is polynomial-time solvable. I don't know if something specific can be made to comment about your problem though.

Factorizing sum of two powers.

2 Answers2