alt Hacker NewsTrue, but there are as many 64-bit integers as pairs of 32-bit integers.
Therefore the fact that relatively few 64-bit numbers are products of 32-bit integers means that a lot of pairs of 32-bit integers give by multiplication the same product.
True, but there are as many 64-bit integers as pairs of 32-bit integers.
Therefore the fact that relatively few 64-bit numbers are products of 32-bit integers means that a lot of pairs of 32-bit integers give by multiplication the same product.
That seems intuitively true given that most 32-bit numbers are composite, so if you have
X = ab and aY < 2^32 and bY < 2^32:
X × Y = X/a × aY = X/b × bY = Y × X = aY × X/a = bY × X/b
Which is 6 pairs resulting in the same product. This will be reduced if e.g. aY = X, but still...