# Only 17% of all 64-bit Integers are products of two 32-bit integers

DevFeed: [Only 17% of all 64-bit Integers are products of two 32-bit integers](<https://devfeed.tech/articles/only-17-of-all-64-bit-integers-are-products-of-two-32-bit-integers-29407.md>)

Original publisher: [Read original article](<https://lemire.me/blog/2026/05/22/only-17-of-all-64-bit-integers-are-products-of-two-32-bit-integers/>)

Author: Daniel Lemire

Published: 2026-05-22T01:16:35Z

Content type: article

Language: en

Sources: [Daniel Lemire](<https://devfeed.tech/sources/daniel-lemire.md>)

Topics: [Programming](<https://devfeed.tech/topics/programming.md>), [hash](<https://devfeed.tech/topics/hash.md>)

Tags: [cryptographic](<https://devfeed.tech/tags/cryptographic.md>), [hash](<https://devfeed.tech/tags/hash.md>), [numbers](<https://devfeed.tech/tags/numbers.md>), [precision](<https://devfeed.tech/tags/precision.md>), [programming](<https://devfeed.tech/tags/programming.md>)

## AI overview

The article examines what fraction of 64-bit integers can be represented as the full product of two 32-bit integers. It presents the result that only 17% can be produced this way and relates the question to hash-function design and multiplication behavior.

## Source excerpt

In software programming, the product between two integers is often computed to a fixed number of bits with overflow. Consider 8-bit integers. If you multiply 127 by 127, you get back the number 1 as an 8-bit unsigned integer, with an overflow. The actual full product is 16129. To represent 16129, you typically use 16 ... Continue reading Only 17% of all 64-bit Integers are products of two 32-bit integers