## Smooth Numbers

Roughly, smooth numbers are integers with small prime factors relative to some bound. Interestingly, these integers find many applications in number theory, but also in graph theory and cryptography, among others.

A first goal of the project would be to gain some experience with smooth integers, by doing some computer calculations and finding possibly some nice patterns. In a second time, the project could allow various different subprojects, such as

- studying several ways of generating smooth integers computationally
- its application to integer factorization. There are algorithms using smooth numbers that allow to factor special cases of composite integers that are products of two primes.
- the study of the set of B-smooth integers within a given range. More generally, one would maybe like to study the distribution of smooth integers in an interval.

The detailed description of the three projects is available for download here.

**Schedule:** Winter semester 2018/2019

**Difficulty level:**
EML 2 (especially for students in their 3rd semester).