YAFU

YAFU
YAFU project logo
Example aliquot sequence graph related to YAFU research
Project
Status	Active
Category	Mathematics, Integer factorization
Compute	CPU
Requires	BOINC
Development
Developer	yoyo
Sponsor	Rechenkraft.net e.V.
Maintainer	YAFU project team
Initial release	January 1, 2012  (14 years ago)
Repository	https://sourceforge.net/projects/yafu/
Software
Written in	C, C++
Operating system	Windows, Linux
Size	~10 MB
BOINC statistics
Stats as of	May 25, 2026  (0 years ago)
Performance	18406.63 GigaFLOPS
Active users	249
Total users	3,020
Active hosts	1,573
Total hosts	45,148
Metadata
Website	https://yafu.myfirewall.org/yafu/
License	GNU General Public License

YAFU is a volunteer distributed computing project based on BOINC that focuses on large scale integer factorization. The project is closely associated with the study of aliquot sequences and uses donated computing power from volunteers around the world to factor composite numbers up to approximately 149 digits in length.

The project uses the YAFU integer factorization software package developed by Ben Buhrow. YAFU integrates several advanced algorithms and external mathematics libraries to automatically select the most efficient factorization method for a given composite number.

Why YAFU?

Integer factorization is an important problem in computational number theory. Many unsolved mathematical questions depend on the ability to decompose very large composite integers into their prime factors. Efficient factorization methods also have practical importance in cryptography, especially in systems such as RSA where security depends on the difficulty of factoring large semiprime numbers.

YAFU contributes to the mathematical study of aliquot sequences, which are iterative sequences formed by repeatedly applying the sum of proper divisors function:

$s(n)=\sigma (n)-n$

where $\sigma (n)$ is the divisor sum function. Beginning with an integer $n$, each subsequent term is generated by summing all proper divisors of the previous term.

Some aliquot sequences terminate at 1, some enter cycles, and others appear to grow indefinitely. Understanding their long term behavior remains an open problem in number theory.

Goal

YAFU's primary goal is to factorize composite numbers arising from ongoing aliquot sequence calculations. The project especially targets composite cofactors up to approximately 149 digits in size in order to extend and maintain known aliquot sequences.

The long term objective is to assist collaborative efforts to bring all known aliquot sequences with starting values below several million to a minimum size threshold of 140 digits or greater. This helps mathematicians determine whether sequences terminate, merge with other sequences, or continue growing.

History

The YAFU BOINC project was launched by the BOINC community member known as "yoyo", who has also operated several other mathematics oriented BOINC projects. The project became associated with the German distributed computing organization Rechenkraft.net e.V., which supports collaborative computational mathematics and citizen science initiatives.

YAFU evolved from standalone factorization work into a BOINC enabled distributed system capable of processing very large batches of integer factorization tasks using volunteer CPU resources.

Methods

YAFU uses several advanced integer factorization algorithms depending on the size and structure of the composite number being processed. These include:

• Elliptic Curve Method (ECM)
• Multiple Polynomial Quadratic Sieve (MPQS)
• General Number Field Sieve (GNFS)
• Pollard's rho algorithm
• Trial division and primality testing

For a composite integer $N$, the project seeks a decomposition of the form:

$N=p_1{p}_2{p}_3\cdots p_n$

where each $p_i$ is prime.

The General Number Field Sieve is currently the fastest known classical algorithm for factoring very large integers and is frequently required for the most difficult YAFU work units.

YAFU uses BOINC because integer factorization workloads can be split into many independent tasks and distributed efficiently across thousands of volunteer computers. This allows the project to achieve computational throughput far beyond what would normally be available to individual researchers or small academic teams.

Unlike many GPU accelerated BOINC projects, YAFU primarily relies on CPU computation because several factorization algorithms benefit heavily from large integer arithmetic performance, memory bandwidth, and highly optimized multi precision libraries.

Volunteer computing

Visualization of an aliquot sequence related to the project.

YAFU is part of the broader BOINC ecosystem of volunteer computing projects. Volunteers install the BOINC client software and receive work units automatically from the project's servers. Completed factorization results are returned to the server and incorporated into larger aliquot sequence databases and factorization records.

The project demonstrates how distributed volunteer computing can contribute to pure mathematics research without requiring centralized supercomputing infrastructure. Participants also contribute to the preservation and extension of public mathematical databases such as FactorDB.

Project team / Sponsors

The project is operated primarily by the BOINC developer and administrator known as "yoyo" with support from Rechenkraft.net e.V., a German nonprofit organization dedicated to distributed computing and scientific volunteer projects.

Scientific significance

Aliquot sequences have been studied since the time of ancient Greek mathematics and remain an active area of research in computational number theory. YAFU contributes computational resources toward understanding several unresolved mathematical questions related to sequence termination, cyclic behavior, and unbounded growth.

The project also contributes benchmark data for evaluating the performance of modern integer factorization algorithms and large scale distributed mathematics applications.

Scientific papers and related publications

Several publications and conference papers related to BOINC, distributed computing, and integer factorization are relevant to YAFU and its computational methods:

• David P. Anderson. "BOINC: A System for Public Resource Computing and Storage."

• Arjen K. Lenstra and Hendrik W. Lenstra Jr. "The Development of the Number Field Sieve."

• Richard Crandall and Carl Pomerance. "Prime Numbers: A Computational Perspective."

See also

• BOINC
• Aliquot sequence
• Integer factorization
• General Number Field Sieve
• FactorDB
• Distributed computing

External links

• Official YAFU project website
• Rechenkraft.net e.V.
• FactorDB
• BOINC
• YAFU source code