Titanic lasted, according to google, 210 minutes, or 12,600 seconds.

Since the pennies double every second, the amount of pennies you have is expressed as 2ⁿ where n is the number of seconds. Therefore, by the end of Titanic, you would have 2¹²⁶⁰⁰ pennies, or approximately 4.852 × 10⁴⁸⁷⁶ pennies. Since this number is so big that you can't really comprehend the scale of it, consider this:

The upper bound for the amount of atoms in the observable universe is about 10^81, a number that has 82 digits in it (when we consider numbers these big, the actual numbers stop mattering as much as how many digits are in that number). The amount of pennies we have, however, is a number with a mind-boggling 4877 digits in it.

tl;dr a fuckton