ODLK2025

ODLK2025
ODLK2025 project logo
Project
Status	Active
Category	Mathematics / Number Theory
Compute	CPU
Development
Developer	Natalia Makarova, termit
Author	Natalia Makarova
Maintainer	termit
Initial release	13 February 2025
Software
Written in	C, C++
Operating system	Windows, Linux
BOINC statistics
Stats as of	22 May 2026
Performance	~1,869 GigaFLOPS (current); ~2,239 GigaFLOPS (total across apps)
Active users	100
Total users	251
Active hosts	307
Total hosts	1,553
Metadata
Website	https://boinc.mak.termit.me/odlk2025/

ODLK2025 is a BOINC-based volunteer computing project that searches for symmetric k-tuples of consecutive prime numbers. It was launched on 13 February 2025 by mathematician Natalia Makarova and server administrator termit, as a continuation and extension of earlier distributed-computing efforts on the same mathematical problem.

Background

Volunteer computing and BOINC

Volunteer computing is an arrangement in which members of the public donate idle CPU cycles on their personal computers to scientific research projects. The Berkeley Open Infrastructure for Network Computing (BOINC) is an open-source middleware system, developed at the University of California, Berkeley, that is the most widely-used platform for such projects. Volunteers install the BOINC client on their computers; the project server then distributes work units, collects results, and awards credits.

Project lineage

ODLK2025 is the latest in a chain of related projects all aimed at symmetric prime tuples:

• T.Brada Experimental Grid (TBEG) — hosted the original "Symmetric Prime Tuples" sub-project, created by Tomáš Brada, which ran until it was discontinued in late 2022.
• Symmetric Prime Tuples (SPT) — a new BOINC project at boinc.termit.me/adsl that continued the work. The SPT application uses the open-source primesieve library to construct a sieve of primes in memory, consuming roughly 1.3 GB RAM per task, then searches for symmetric tuples within the range up to $2^{64}$.
• ODLK2025 — launched when the need arose to search beyond the $2^{64}$ limit that constrains SPT, and when disagreements over adding a new application algorithm to SPT led Makarova and termit to establish an independent project.

ODLK2025 also continues work previously done in ODLK (boinc.progger.info/odlk) and is described on its own homepage as "a new fork from" TBEG, SPT, and ODLK.

Note: BOINC's creator, David Anderson, declined to add ODLK2025 to the official BOINC project list, citing a preference against "overlapping" projects. The project is therefore independently hosted and listed on community sites such as BOINC Synergy.

Why ODLK2025?

The Ulam spiral, a visualisation of the distribution of prime numbers, illustrating the clustering phenomena that motivate the search for prime tuples.

ODLK2025 is a subproject of the BOINC project Symmetric Prime Tuples (SPT).

ODLK2025 solves the problem of finding symmetric tuples of consecutive prime numbers which cannot be found in the BOINC project SPT due to the search range limitation to $2^{64}$.

In particular, the problem of finding symmetric tuples of length 17 of consecutive prime numbers according to the following pattern:

$0,6,24,36,66,84,90,114,120,126,150,156,174,204,216,234,240$

The existence of such tuples is a necessary condition for the existence of a symmetric tuple of length 19 of consecutive prime numbers with a minimum diameter of 252.

Currently, this sub-problem is also being discussed in a non-BOINC context at the dxdy.ru forum topic "Symmetric tuples of consecutive prime numbers".

Goal

The primary goal of ODLK2025 is to find symmetric k-tuples of consecutive prime numbers in search ranges that exceed $2^{64}$, which is the limit of the parent SPT project. The project pursues the following concrete targets:

• Find symmetric 17-tuples of consecutive primes matching the pattern $0,6,24,36,66,84,90,114,120,126,150,156,174,204,216,234,240$ — a necessary precondition for demonstrating the existence of a symmetric 19-tuple with minimum diameter 252.
• Search for symmetric 19-tuples (Calc19Tuples application) and 21-tuples (Calc21Tuples) in higher ranges.
• Search for symmetric 15-tuples via the Calc15Tuples application, which uses an algorithm by Makarova that allows the search to be completed exhaustively over a defined range.

Mathematical background

The prime-counting function $\pi (x)$, illustrating the density of primes - the raw material for prime tuple searches.

The mathematical foundations of ODLK2025 rest on the theory of prime k-tuples and the Hardy–Littlewood conjectures.

The Hardy–Littlewood conjecture

In 1923, G. H. Hardy and J. E. Littlewood proposed a conjecture giving the asymptotic density of admissible prime k-tuples. If ${\mathscr{H}}=(a_1,a_2,\dots ,a_k)$ is an admissible pattern (one that does not cover all residues for any prime), the conjecture predicts that the count of primes $p\le n$ for which $p+a_1,\dots ,p+a_k$ are all prime is asymptotically

${\pi }_{{\mathscr{H}}}(n)\sim \mathfrak{𝔖}({\mathscr{H}})\underset{2}{\overset{n}{\int }}\frac{dt}{(\log t{)}^{k+1}}$

where $\mathfrak{𝔖}({\mathscr{H}})$ is the Hardy–Littlewood singular series (a product over primes reflecting local density corrections). This conjecture remains unproven but is strongly supported by numerical evidence.

Problem 62

The specific research problem addressed by ODLK2025 was originally formulated by Natalia Makarova and published as "Problem 62. Symmetric k-tuples of consecutive primes" on the PrimePuzzles.net website. The definitions below are taken from that problem statement.

Methods

Definition 1: Prime k-tuple

A prime k-tuple is a finite collection of values $(p+a_1,p+a_2,p+a_3,\dots ,p+a_k)$, where $p,p+a_1,p+a_2,\dots ,p+a_k$ are prime numbers and $(a_1,a_2,a_3,\dots ,a_k)$ is called the pattern. Typically the first value in the pattern is 0 and the rest are distinct positive even numbers. We consider the k-tuple where $p+a_1,p+a_2,\dots ,p+a_k$ are consecutive primes.

Definition 2: Symmetric k-tuple (even length)

A k-tuple $(p+a_1,p+a_2,\dots ,p+a_{k/2},p+a_{k/2+1},\dots ,p+a_{k-1},p+a_k)$ for even $k$ is called symmetric if

$a_1+a_k=a_2+a_{k-1}=a_3+a_{k-2}=\cdots =a_{k/2}+a_{k/2+1}.$

Example — symmetric 8-tuple:

$17:0,2,6,12,14,20,24,26$

which is short for $(17+0,17+2,17+6,17+12,17+14,17+20,17+24,17+26)$.

Definition 3: Symmetric k-tuple (odd length)

A k-tuple for odd $k$ is called symmetric if

$a_1+a_k=a_2+a_{k-1}=\cdots =a_{(k-1)/2}+a_{(k-1)/2+2}=2a_{(k-1)/2+1}.$

Example — symmetric 5-tuple:

$18713:0,6,18,30,36$

Definition 4: Diameter

The diameter $d$ of a k-tuple is the difference between its largest and smallest elements.

Example — the 8-tuple $17:0,2,6,12,14,20,24,26$ has diameter $d=26$.

Applications

The project currently runs four CPU-only applications for Windows (x86-64) and Linux (x86-64):

Application	Description	Version	Avg. performance (Windows / Linux)
Calculate Tuples	Original symmetric-tuple search application (now suspended to save resources)	2.95	182 / 122 GigaFLOPS
Calc19Tuples	Searches for symmetric 19-tuples	2.18	629 / 169 GigaFLOPS
Calc21Tuples	Searches for symmetric 21-tuples	1.16	862 / 203 GigaFLOPS
Calc15Tuples	Searches for 15-tuples (and sub-tuples 9, 11, 13) using Makarova's exhaustive algorithm	1.05	38 / 35 GigaFLOPS

The total average computing power across all applications is approximately 2,239 GigaFLOPS.

All applications are CPU-only. GPU support is not currently offered.

Server status (as of 22 May 2026)

The following statistics were read directly from the project server status page:

Metric	Value
Users with credit	251
Users with recent credit	100
Computers with credit	1,553
Computers with recent credit	307
Current performance	~1,869 GigaFLOPS
Tasks in progress	12,098
Tasks ready to send	8,207

All server daemons (scheduler, feeder, transitioner, validators, assimilators, file deleter) are reported as Running.

How to participate

1. Download and install the BOINC client for your operating system (Windows or Linux).
2. In the BOINC Manager, choose Add Project and enter the URL: https://boinc.mak.termit.me/odlk2025/
3. Create an account, and BOINC will automatically download work units and begin computing.

Each task currently runs for an average of 1.5–3 hours depending on application. Tasks are CPU-only and require no GPU.

Project team / Sponsors

• Natalia (Nataliya) Makarova — Project scientist; originator of Problem 62 and the underlying algorithms.
• termit — Project administrator; operates the server infrastructure.

Related projects

• Symmetric Prime Tuples (SPT) — the parent BOINC project; searches up to $2^{64}$
• ODLK — earlier project at progger.info hosting related tuple work
• PrimeGrid — a major BOINC project searching for prime numbers of various forms
• Gerasim@Home — also runs a "Get Symmetrical Tuples" application using a different algorithm (odd-length tuples only)

Results repository

Computed results (found tuples) are stored in the project's public database:

• ODLK2025 Results Repository

Related scientific papers

• Volfson, Victor.Dependencies of prime numbers in a tuple. arXiv. — Analyses the Hardy–Littlewood constant for symmetric tuples and proves that it decreases monotonically as tuple length decreases, reflecting weakening inter-prime dependence.
• Tóth, László.On The Asymptotic Density Of Prime k-tuples and a Conjecture of Hardy and Littlewood. arXiv. — Computes "Skewes numbers" for nine prime k-tuples and provides numerical support for the Hardy–Littlewood conjecture.
• Anderson, David P..(2019}).BOINC: A Platform for Volunteer Computing. Journal of Grid Computing. DOI: 10.1007/s10723-019-09497-9. — Describes the BOINC platform on which ODLK2025 runs.

See also

• Prime k-tuple
• First Hardy–Littlewood conjecture
• BOINC
• Volunteer computing
• PrimeGrid
• Twin prime

External links

• ODLK2025 official project page
• ODLK2025 server status
• Results repository
• Problem 62: Symmetric k-tuples of consecutive primes (primepuzzles.net)
• Symmetric tuples of consecutive prime numbers (dxdy.ru forum, in Russian)
• Symmetric Prime Tuples (SPT) — parent BOINC project
• ODLK2025 on BOINC Synergy