[saghm]

The way the headline is phrased doesn't really surprise me much. There aren't twice as many 64-bit integers than 32-bit ones; there are twice as many 33-bit integers as 32 bit ones, and there are 2^32 times as many 64-bit ones than 32-bit ones. It's like asking how many numbers between 1-64 you can get by multiplying numbers between 1-8; I think it's readily apparent that a pretty large portion are missed.

[andrewflnr]

But you're using two 32-bit numbers, which have the same total bits as a 64-bit number. There are equally many 32-bit x 32-bit pairs as there are 64-bit numbers.

[saghm]

And there are as many pairs of numbers between 1-8 and numbers from 1-64, but it's still pretty apparent that most of them are not represented in the set of products.