I'm not sure I understand your comment. Just because a number of of the form 2N with N > 2^32 doesn't mean it can't also be written as the product of two number

I'm not sure I understand your comment. Just because a number of of the form 2N with N > 2^32 doesn't mean it can't also be written as the product of two numbers below 2^32. E.g. 2^40 = 2^20 * 2^20