In this repository we provide some code for solving Modular Subset Product Problem.
We apply this problem to find Carmichael numbers by using Erdos algorithm (which uses MSPP), see section 3 of paper. Published as:
K. A. Draziotis, V. Martidis and S. Tiganourias, Product Subset Problem : Applications to number theory and cryptography, Book Chapter, Analysis, Cryptography and Information Science, Chapter 5, Vol. 10, World Scientific, 2023. https://www.worldscientific.com/worl... Applications of MSPP to cryptography see here

We provide Sagemath code, which we used to build all the (small instances) tables.

We also provide c++ single and multi core variants. Using the single core case we managed to produce a Carmichael number with 19589 prime factors in a I5/16Gb Linux PC in three hours.

We provide tables for Carmichael numbers in directory Tables.

For instance,

5-80.txt contains Carmichael numbers with 5 to 80 prime factors.

2542.txt contains a Carmichael number with 2542 prime factors.

You can download the source code with the tables by using

git clone https://github.com/drazioti/Carmichael.git

First fork this repository. Make the changes you want (e.g. update some tables, correct a bug to the code etc)