TITLE: How to prove that a very large number is not prime
QUESTION [27 upvotes]: I'm solving few math problems for an upcoming math contest .
I am stuck with a short problem, where I have to prove that $A$ is not prime .
$$A = 100\ 000\ 000\ 000\ 000\ 000\ 001$$
$A$ is not a binary number. It's a decimal one.
I've tried to rewrite like this:
$$ A = 1 \times 10^{20} + 1 $$
But what can I do with that . I can't use GCD since it would a very long time to finish it and Obviously this isn't the point from this problem .

REPLY [5 votes]: $x^5+1 = (x+1)(x^4 - x^3 + x^2 - x + 1)$  (and this will work for any odd power.
replace $x$ with $10^4$
$10^4+1$ divides $10^{20}+1$