Modulo settings for successful encryption?

I saw this awesome video which shows how encryption works using "discrete logarithm".

The example says: $3^x\mod17$. I understood that $3$ is called “generator”, because it has no "straight" root and when used with any exponents it walks through entire clock (till $17$ in that case).

1. Would saying $3^x \mod 449825$ make it any weaker, easier to crack, or anything alike? Is there anything I should watch out for when choosing that number?
2. If it's a logarithm, why is it the function having $\mod x$ in it? I have $\log(x)$ on my calculator, not $\mod x$. Is it correct that $\mod x$ stands for modulo?
• 1) yes, 449825 is not a prime. 2) its a discrete logarithm (one in a finite field - in your first example a prime field - and not in the reals). – DrLecter Jun 21 '14 at 23:55
• You can emulate mod on a calculator like so: to compute a mod b, compute a/b, round it down, multiply b by the result and subtract a from it. E.g. for 77 mod 8, 77 / 8 = 9.62, so we have 77 mod 8 = 77 - 8 * 9 = 5. Or you can just multiply the fractional part by b, but you tend to run into precision issues quicker doing it that way. – Thomas Jun 22 '14 at 5:24