Of course you mean numbers of the form 2^(2^n) + 1; without the increment, primality is easy to check. :-) Anyway, are you sure that it would be so easy to check primality of 15-decimal-digit numbers without even a pocket calculator, especially with no guarantee that there was any reason to do so? (Notice, for example, that you needed to add "if someone told me to".)

For more on this, see KConrad's comment https://matheducators.stackexchange.com/questions/16636/is-t... and kcrisman's comment https://matheducators.stackexchange.com/questions/16636/is-t... on the post linked by your parent.