alt Hacker NewsHaving a prime factor greater than 2^32 accounts for about 80% of the 64-bit integers that can’t be expressed as a product of 32-bit integers. But it’s not the only way; you can also have three prime factors in the range (2^16, 2^32), for instance.
Having a prime factor greater than 2^32 accounts for about 80% of the 64-bit integers that can’t be expressed as a product of 32-bit integers. But it’s not the only way; you can also have three prime factors in the range (2^16, 2^32), for instance.
More precisely one in the range (a,2^32) and two in the range (2^32/a, 2^32). But if the latter have many duplicate prime factors it's worse.