SRBase

SRBase
SRBase project logo
Project
Status	Active
Category	Mathematics / Number Theory
Compute	CPU & GPU
Development
Developer	rebirther
Author	rebirther
Sponsor	Conjectures 'R Us (CRUS), GIMPS
Maintainer	rebirther
Initial release	January 2, 2013  (13 years ago)
Software
Written in	C, C++
Operating system	Windows, Linux, macOS
Metadata
Website	https://srbase.my-firewall.org/sr5/
License	BOINC Confederation

SRBase is a BOINC-based volunteer computing project focused on mathematical research in number theory. It enlists the spare processing power of volunteers' computers around the world to prove the generalized Sierpinski and Riesel conjectures for all integer bases $b\le 1030$, working on cases not currently addressed by other distributed computing efforts.

Mathematical background

The Sierpinski conjecture

Wacław Sierpiński. (1882–1969), the Polish mathematician who proved the existence of infinitely many Sierpiński numbers in 1960.

In number theory, a Sierpiński number is an odd natural number $k$ such that $k\times 2^n+1$ is composite for all natural numbers $n$. In 1960, Wacław Sierpiński proved that there are infinitely many odd integers $k$ which have this property. In other words, for a Sierpiński number $k$, no matter what positive integer is substituted for $n$, the result is always a composite (non-prime) number. "There's no obvious reason why they should exist," as mathematician Chris Caldwell has noted; for most values of $k$, primes appear quite regularly in the sequence $k\cdot 2^n+1$.

The number 78,557 was proved to be a Sierpiński number by John Selfridge in 1962, who showed that all numbers of the form $78557\cdot 2^n+1$ have a factor in the covering set $\{3,5,7,13,19,37,73\}$. In 1967, it was conjectured by Sierpiński and Selfridge that 78,557 is the smallest Sierpiński number. To solve the Sierpiński problem fully, one needs to prove that for every odd number $k<78,557$, there exists an $n$ such that $k\cdot 2^n+1$ is a prime number.

SRBase extends this classical question to all integer bases up to 1030, so for any base $b$ in the Sierpiński (+1) form, a conjectured minimum Sierpiński value is the smallest $k$ for which $k\cdot b^n+1$ is composite for every $n\ge 1$.

The Riesel conjecture

Hans Ivar Riesel (28 May 1929 in Stockholm – 21 December 2014) was a Swedish mathematician who discovered the 18th Mersenne prime in 1957 using the computer BESK: $2^{3217}-1$, comprising 969 digits. Intrigued by numbers that resist such searches, he proved in 1956 that there exist odd integers $k$ for which $k\cdot 2^n-1$ is composite for every $n\ge 1$, inaugurating the study of what are now called Riesel numbers.

Hans Riesel showed that there are an infinite number of integers $k$ such that $k\cdot 2^n-1$ is not prime for any integer $n$. He showed that the number 509,203 has this property. The Riesel problem consists in determining the smallest Riesel number. Because no covering set has been found for any $k$ less than 509,203, it is conjectured to be the smallest Riesel number.

Analogously to the Sierpiński problem, SRBase generalizes this to the Riesel (−1) form $k\cdot b^n-1$ for every base $b\le 1030$, seeking the conjectured minimum Riesel value for each base.

The generalized conjecture

Conjectures 'R Us (CRUS) was established in 2007 by Gary Barnes. For every base $b\le 1030$ for the forms $k\cdot b^n\pm 1$, there is a $k$-value for each form that has been conjectured to be the lowest "Sierpiński value" (+1 form) or "Riesel value" (−1 form) that is composite for all values of $n\ge 1$. A conjecture is proven when a prime is found for every $k$ below the conjectured minimum value, eliminating each candidate in turn. SRBase serves as the BOINC-powered computational arm of this effort.

Goal

The project's mission is to prove the Riesel and Sierpiński conjectures for all bases $b\le 1030$ that are not already being worked on by other projects or efforts. For every base $b$, the two target forms are:

• Sierpiński (+1): $k\cdot b^n+1$
• Riesel (−1): $k\cdot b^n-1$

The project seeks the lowest value of $k$ in each form that is composite for all $n\ge 1$, and then eliminates each smaller candidate by finding a prime. A base is declared "proven" when all such candidates have been eliminated.

History

SRBase was launched in 2014, as indicated by its copyright notice "© 2014–2026 BOINC Confederation / rebirther." It is administered by a volunteer known by the handle rebirther, who runs the project server on a private computer inside a virtual machine — famously rumored to reside in a closet.

The project has maintained a steady annual review of its progress since its founding. Over its first nine years, 28 bases were proven, with the number of unstarted bases declining from 314 in 2014–2015 to 69 by 2022–2023. The following table summarizes yearly progress through 2023:

Year	Bases proven	Unstarted bases remaining
2014–2015	1	314
2015–2016	5	297
2016–2017	5	282
2017–2018	1	264
2018–2019	6	218
2019–2020	4	120
2020–2021	3	101
2021–2022	0	97
2022–2023	3	69
Total (9 years)	28	69

Methods and technology

Applications

SRBase distributes computational work to volunteers via the BOINC client. The core computation involves primality testing of candidate numbers of the forms $k\cdot b^n\pm 1$. The project has migrated from the LLR2 application to PRST (a similar application already used at PrimeGrid), which was intended to replace LLR2 and brings performance improvements and better hardware support. Recent application milestones include updating to PRST v10, multi-GPU sieving, and support for Intel Arc GPUs.

Both CPU and GPU work units are available. The PRST application supports modern instruction sets including AVX-512 for compatible processors, allowing significantly faster computations on modern hardware.

Sieving

Before primality testing, candidate numbers are sieved to eliminate those with small factors, reducing the amount of expensive primality work. SRBase makes use of sieving in collaboration with the yoyo@home project. It should be noted that SRBase is the BOINC side of the CRUS (Conjectures 'R Us) project, which is also connected with the sieve application at Yoyo.

Infrastructure

The project server is hosted on a private machine running inside a virtual machine. This unconventional setup has become a point of gentle pride within the volunteer computing community. Work reservation and preparation are coordinated via the Mersenne Forum at mersenneforum.org, where users reserve bases to avoid duplicate effort. Results processing and prime removal from sieve files are handled using the srfile application.

Collaborations

SRBase operates in active collaboration with two major mathematical computing projects:

Conjectures 'R Us (CRUS)

The Conjectures 'R Us project works to prove the Riesel and Sierpiński conjectures for all bases $\le 1030$ that are not being handled by other projects. Testing is coordinated through the Mersenne forum at mersenneforum.org, where $k$-values and bases can be reserved and tested. SRBase serves as the BOINC-powered computational engine for CRUS. Work reservations are filed through the Mersenne Forum to ensure no base is tested twice by different contributors.

Great Internet Mersenne Prime Search (GIMPS)

SRBase has created a BOINC project to hand out trial factoring assignments on large Mersenne numbers. These are very quick work units. Specifically, SRBase's GPU trial factoring effort covers Mersenne numbers in the 100–1000 million exponent range and has progressed through successive bit levels of trial division, working collaboratively with the broader GIMPS effort coordinated through PrimeNet.

Project team

SRBase is maintained by a small, dedicated team of volunteer contributors:

Handle	Role
rebirther	SRBase admin; server and application management
Gary (Gary Barnes)	Mersenne/CRUS admin; results processing
Prime95 (George Woltman)	GIMPS admin; work distribution
Odicin	Scripts
walli	Coding
deletenull	GPU applications and compilation

Gary Barnes founded the Conjectures 'R Us project in 2007 and coordinates the mathematical side of the collaboration. George Woltman, creator of the Prime95 software and co-founder of GIMPS in 1996, assists with work distribution for the trial factoring subproject.

Scientific results and notable finds

Proven bases and conjecture progress

As of early 2021, SRBase had reported 400 of 1,031 Riesel bases proven and 390 of 1,032 Sierpiński bases proven, with 112 bases still unstarted. Progress statistics are maintained by the CRUS project at noprimeleftbehind.net.

• Overall CRUS statistics
• Riesel reservations
• Sierpiński reservations

Megaprime discoveries

SRBase participants have discovered numerous megaprimes (primes with over one million decimal digits), which are automatically submitted to the Top 5000 Largest Known Primes Database (T5k PrimePages). Notable recent discoveries include:

• 163 * 778^424575 + 1 (1,227,440 digits) — found by Nexhr of team Gridcoin, a megaprime for base S778.
• 84 * 730^560037 + 1 (1,603,569 digits) — found by Oliver Kruse, a megaprime for base S730.
• 78 * 622^402915 - 1 (1,125,662 digits) — found by IDEA of team Idea Digital Imaging; this find also proved base R622.
• 543131 * 2^3529754 - 1 (1,062,568 digits) — found by zlodeck of team Russia, a megaprime for the R2 second conjecture.
• 1676 * 199^460981 - 1 (1,059,731 digits) — found by Sightus@CAU of team Planet 3DNow!, entered the T5k PrimePages in February 2026.

Published guide

The project has produced an internal reference document, Behind SRBase — A Short Guide, available at the project website. This guide chronicles BOINC server administration notes, work-unit generation procedures, and the workflow used to move bases from the CRUS reservation system through sieving and primality testing to a verified prime. It is described as a practical record of the operational knowledge built up over the project's lifetime.

Participation

Joining the project

To join SRBase, participants download BOINC, select "Add Project," and enter the URL https://srbase.my-firewall.org/sr5/. The project invitation code for creating new accounts is pillepalle.

BOINC Pentathlon

SRBase has been selected multiple times as one of the five projects in the annual BOINC Pentathlon, a competitive volunteer computing event in which teams race to accumulate the most credit across several projects over a two-week period. In the 2025 BOINC Pentathlon, SRBase was selected for the three-day Sprint discipline. It was also the Sprint project for the 2022 Pentathlon.

Gridcoin

SRBase is whitelisted by the Gridcoin network, allowing participants who hold Gridcoin cryptocurrency to earn rewards proportional to their verified scientific computing contributions to the project.

See also

• PrimeGrid
• Great Internet Mersenne Prime Search (GIMPS)
• Sierpiński number
• Riesel number
• Berkeley Open Infrastructure for Network Computing (BOINC)
• Seventeen or Bust

External links

• SRBase project homepage
• Conjectures 'R Us project page
• Mersenne Forum: CRUS base reservations
• Behind SRBase – A Short Guide (PDF)
• SRBase news feed at BOINCstats