NFS@Home is a research project that uses Internet-connected computers to do the lattice sieving step in the Number Field Sieve factorization of large integers.
As a young school student, you gained your first experience at breaking an integer into prime factors, such as 15 = 3 * 5 or 35 = 5 * 7. NFS@Home is a continuation of that experience, only with integers that are hundreds of digits long. Most recent large factorizations have been done primarily by large clusters at universities or AI companies. With NFS@Home you can participate in state-of-the-art factorizations simply by downloading and running a free program on your computer.
Factoring a number this large is done in stages. Sieving is the stage that parallelises well across many independent computers, which is what makes it suited to volunteer computing: each workunit covers its own slice of the search space and needs no contact with the others. The later stages, linear algebra and the square root, are run on dedicated hardware afterwards.
You can see what is being sieved at the moment, and how far along each number is, on the front page or in more detail on the per-application status pages:
The applications differ in the sieving parameters they use, and therefore in how much memory and time a workunit needs. Applications lists the versions and platforms currently available, and you can choose which ones your computer takes on in your project preferences. cudasieve is the newest of them, a GPU implementation still under test.
Integer factorization is interesting from both mathematical and practical perspectives. Mathematically, for instance, the calculation of multiplicative functions in number theory for a particular number require the factors of the number. Likewise, the integer factorization of particular numbers can aid in the proof that an associated number is prime. Practically, many public key algorithms, including the RSA algorithm, rely on the fact that the publicly available modulus cannot be factored. If it is factored, the private key can be easily calculated. Until quite recently, RSA-512, which uses a 512-bit modulus (155 digits), was commonly used but can now be easily broken.
Many of the numbers that we are factoring are chosen from the Cunningham project. Started in 1925, it is one of the oldest continuously ongoing projects in computational number theory. The third edition of the book, published by the American Mathematical Society in 2002, is available as a free download. All results obtained since, including those of NFS@Home, are available on the Cunningham project website.
Completed factorizations are listed on Status of numbers, together with the size of the factors found and a link to the full result for each one. Notable results are announced on the message boards.
The project runs on BOINC, which runs the work in the background and only when you are not using the machine yourself. To join:
There is no minimum commitment, and you can stop at any time. Credit for completed work is tracked per application, and statistics are published for individuals and teams.
NFS@Home is hosted at California State University Fullerton, and is supported in part by the National Science Foundation through ACCESS resources provided by the Texas Advanced Computing Center, the San Diego Supercomputer Center, the National Center for Supercomputing Applications, and Purdue University under grant number DMS100027.
The post-processing that turns sieving results into factors is carried out on those resources. Volunteers who have made particular contributions to the project are acknowledged on the special contributions page.