I must be missing something. Aren’t ~50% of 64-bit integers the product of the number 2 and another 32-bit integer?
I don’t think so, because that only gets you up to 2x2^32, which is nowhere near halfway to 2^64
No. 50% of them are the product of 2 and a 63-bit integer.
Going from 32 bits to 64 bits doesn't double the range (that would be adding 1 bit), it squares the range.