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<div style="background-color: #D4E2FC; border-top: 1px solid #5F92F2; font-size: bigger; padding-left: 15px; margin: 12px -5px -5px -5px;">'''BOINC project page template'''</div>
{{Infobox software
| name                = ODLK2025
| logo                = Odlk2025.jpg
| logo caption        = ODLK2025 project logo


[[File:{{#setmainimage:Odlk2025.jpg|409x180px}}|alt=logo image|center|frameless]][https://boinc.mak.termit.me/odlk2025/ '''''ODLK2025'''''] is a BOINC based '''''[[wikipedia:Volunteer computing|volunteer computing]]''''' project that needs your help to search for Symmetric k-Tuples of consecutive Primes.
| status              = Active
| category            = Mathematics / Number Theory
| compute              = CPU
 
| author              = Natalia Makarova
| developer            = Natalia Makarova, termit
| maintainer          = termit
| released            = 13 February 2025
 
| programming language = C, C++
| operating system    = Windows, Linux
 
| stats as of          = 22 May 2026
| active users        = 100
| total users          = 251
| active hosts        = 307
| total hosts          = 1553
 
| average performance  = ~1,869 GigaFLOPS (current); ~2,239 GigaFLOPS (total across apps)
 
| website              = {{URL|https://boinc.mak.termit.me/odlk2025/}}
}}
 
[https://boinc.mak.termit.me/odlk2025/ '''''ODLK2025'''''] is a [[wikipedia:Berkeley Open Infrastructure for Network Computing|BOINC]]-based '''''[[wikipedia:Volunteer computing|volunteer computing]]''''' project that searches for symmetric [[wikipedia:Prime k-tuple|''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.<ref name="tbrada_launch">{{cite web |url=https://boinc.tbrada.eu/old_news.php |title=News archive — T.Brada Experimental Grid |accessdate=2026-05-22}}</ref>
 
== Background ==
 
=== Volunteer computing and BOINC ===
 
[[wikipedia:Volunteer computing|Volunteer computing]] is an arrangement in which members of the public donate idle CPU cycles on their personal computers to scientific research projects.<ref name="boinc_paper">{{cite journal |author=Anderson, David P. |title=BOINC: A Platform for Volunteer Computing |journal=Journal of Grid Computing |year=2019 |doi=10.1007/s10723-019-09497-9}}</ref> The [[wikipedia:Berkeley Open Infrastructure for Network Computing|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.<ref name="boinc_wiki">{{cite web |url=https://en.wikipedia.org/wiki/Berkeley_Open_Infrastructure_for_Network_Computing |title=Berkeley Open Infrastructure for Network Computing — Wikipedia |accessdate=2026-05-22}}</ref> 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.<ref name="tbrada_launch"/>
* '''Symmetric Prime Tuples (SPT)''' — a new BOINC project at <code>boinc.termit.me/adsl</code> that continued the work. The SPT application uses the open-source [[wikipedia:primesieve|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 <math>2^{64}</math>.<ref name="boincsynergy_spt">{{cite web |url=https://boincsynergy.ca/wiki/index.php?title=SPT |title=SPT — BOINC Synergy Wiki |accessdate=2026-05-22}}</ref>
* '''ODLK2025''' — launched when the need arose to search beyond the <math>2^{64}</math> limit that constrains SPT, and when disagreements over adding a new application algorithm to SPT led Makarova and termit to establish an independent project.<ref name="formulaboinc">{{cite web |url=https://www.formula-boinc.org/forum/viewtopic.php?t=418&start=20 |title=Marathon 2025 — FormulaBoinc Forum |date=2025-01-25 |accessdate=2026-05-22}}</ref>
 
ODLK2025 also continues work previously done in '''ODLK''' (<code>boinc.progger.info/odlk</code>) and is described on its own homepage as "a new fork from" TBEG, SPT, and ODLK.<ref name="odlk2025_home">{{cite web |url=https://boinc.mak.termit.me/odlk2025/ |title=ODLK2025 — What is ODLK2025? |accessdate=2026-05-22}}</ref>
 
Note: BOINC's creator, David Anderson, declined to add ODLK2025 to the official BOINC project list, citing a preference against "overlapping" projects.<ref name="boinc_berkeley_thread">{{cite web |url=https://boinc.berkeley.edu/forum_thread.php?id=15423 |title=Thread: New project ODLK2025 — BOINC message boards |date=2025-01-20 |accessdate=2026-05-22}}</ref> The project is therefore independently hosted and listed on community sites such as BOINC Synergy.


== Why ODLK2025? ==
== Why ODLK2025? ==
[[File:Spirale Ulam 150.jpg|thumb|305x305px|The [[wikipedia:Ulam spiral|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 [https://boinc.termit.me/adsl/ 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 <math>2^{64}</math>.
In particular, the problem of finding symmetric tuples of length 17 of consecutive prime numbers according to the following pattern:


The ODLK25 is a subproject of the BOINC project [https://boinc.termit.me/adsl/ Symmetric Prime Tuples (SPT)]
: <math>0, 6, 24, 36, 66, 84, 90, 114, 120, 126, 150, 156, 174, 204, 216, 234, 240</math>
 
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 [https://dxdy.ru/topic100750.html dxdy.ru forum topic "Symmetric tuples of consecutive prime numbers"].


== Goal ==
== Goal ==


The project 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.
The primary goal of ODLK2025 is to find symmetric [[wikipedia:Prime k-tuple|''k''-tuples]] of consecutive prime numbers in search ranges that exceed <math>2^{64}</math>, which is the limit of the parent SPT project. The project pursues the following concrete targets:


In particular, the problem of finding symmetric tuples of length 17 of consecutive prime numbers according to the following pattern
* Find symmetric 17-tuples of consecutive primes matching the pattern <math>0, 6, 24, 36, 66, 84, 90, 114, 120, 126, 150, 156, 174, 204, 216, 234, 240</math> — 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.<ref name="odlk2025_news">{{cite web |url=https://boinc.mak.termit.me/odlk2025/ |title=ODLK2025 News — Calc15Tuples launched |date=2025-07-12 |accessdate=2026-05-22}}</ref>


0, 6, 24, 36, 66, 84, 90, 114, 120, 126, 150, 156, 174, 204, 216, 234, 240
== Mathematical background ==
[[File:PrimePi.svg|thumb|305x305px|The [[wikipedia:Prime-counting function|prime-counting function]] <math>\pi(x)</math>, illustrating the density of primes - the raw material for prime tuple searches.]]
The mathematical foundations of ODLK2025 rest on the theory of [[wikipedia:Prime k-tuple|prime ''k''-tuples]] and the [[wikipedia:First Hardy–Littlewood conjecture|Hardy–Littlewood conjectures]].<ref name="hl_conjecture">{{cite web |url=https://en.wikipedia.org/wiki/First_Hardy%E2%80%93Littlewood_conjecture |title=First Hardy–Littlewood conjecture — Wikipedia |accessdate=2026-05-22}}</ref>


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.
=== 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.<ref name="hl_original">{{cite journal |author=Hardy, G. H.; Littlewood, J. E. |title=Some Problems of 'Partitio Numerorum.' III. On the Expression of a Number as a Sum of Primes |journal=Acta Mathematica |volume=44 |pages=1–70 |year=1923}}</ref> If <math>\mathcal{H} = (a_1, a_2, \ldots, a_k)</math> is an admissible pattern (one that does not cover all residues for any prime), the conjecture predicts that the count of primes <math>p \leq n</math> for which <math>p+a_1, \ldots, p+a_k</math> are all prime is asymptotically


Currently, this subproblem is being solved in a non-BOINC project
:<math>\pi_{\mathcal{H}}(n) \sim \mathfrak{S}(\mathcal{H}) \int_2^n \frac{dt}{(\log t)^{k+1}}</math>


https://boinc.termit.me/adsl/forum_thread.php?id=79
where <math>\mathfrak{S}(\mathcal{H})</math> 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.<ref name="toth_arxiv">{{cite web |url=https://arxiv.org/abs/1910.02636 |title=On The Asymptotic Density Of Prime k-tuples and a Conjecture of Hardy and Littlewood |author=Tóth, László |year=2019 |accessdate=2026-05-22}}</ref>


https://boinc.progger.info/odlk/forum_thread.php?id=293
=== Problem 62 ===


The problem of finding a symmetrical 19-tuplet with a minimum diameter of 252 is being solved by a group of participants of the dxdy.ru forum.
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.<ref name="prob62">{{cite web |url=https://www.primepuzzles.net/problems/prob_062.htm |title=Problem 62. Symmetric k-tuples of consecutive primes — primepuzzles.net |accessdate=2026-05-22}}</ref> The definitions below are taken from that problem statement.


See the topic "Symmetric tuples of consecutive prime numbers" https://dxdy.ru/topic100750.html
== Methods ==
== Methods ==


==== Definition 1 ====
=== Definition 1: Prime ''k''-tuple ===
A prime k-tuple is a finite collection of values (p + a1, p + a2, p + a3, …, p + ak),
 
A prime ''k''-tuple is a finite collection of values <math>(p + a_1,\; p + a_2,\; p + a_3,\; \ldots,\; p + a_k)</math>, where <math>p,\; p + a_1,\; p + a_2,\; \ldots,\; p + a_k</math> are prime numbers and <math>(a_1, a_2, a_3, \ldots, a_k)</math> is called the '''pattern'''. Typically the first value in the pattern is 0 and the rest are distinct positive even numbers.<ref name="prob62"/> We consider the ''k''-tuple where <math>p + a_1, p + a_2, \ldots, p + a_k</math> are '''consecutive''' primes.
 
=== Definition 2: Symmetric ''k''-tuple (even length) ===
 
A ''k''-tuple <math>(p + a_1,\; p + a_2,\; \ldots,\; p + a_{k/2},\; p + a_{k/2+1},\; \ldots,\; p + a_{k-1},\; p + a_k)</math> for even <math>k</math> is called '''symmetric''' if
 
:<math>a_1 + a_k \;=\; a_2 + a_{k-1} \;=\; a_3 + a_{k-2} \;=\; \cdots \;=\; a_{k/2} + a_{k/2+1}.</math>
 
'''Example''' — symmetric 8-tuple:
 
:<math>17:\; 0,\; 2,\; 6,\; 12,\; 14,\; 20,\; 24,\; 26</math>
 
which is short for <math>(17+0,\; 17+2,\; 17+6,\; 17+12,\; 17+14,\; 17+20,\; 17+24,\; 17+26)</math>.
 
=== Definition 3: Symmetric ''k''-tuple (odd length) ===
 
A ''k''-tuple for odd <math>k</math> is called '''symmetric''' if
 
:<math>a_1 + a_k \;=\; a_2 + a_{k-1} \;=\; \cdots \;=\; a_{(k-1)/2} + a_{(k-1)/2+2} \;=\; 2\,a_{(k-1)/2+1}.</math>
 
'''Example''' — symmetric 5-tuple:
 
:<math>18713:\; 0,\; 6,\; 18,\; 30,\; 36</math>


where p, p + a1, p + a2, p + a3, …, p + ak are prime numbers, (a1, a2, a3, …, ak) are pattern. Typically the first value in the pattern is 0 and the rest are distinct positive even numbers. [1]
=== Definition 4: Diameter ===


We consider the k-tuple, where p + a1, p + a2, p + a3, ..., p + ak are consecutive primes.
The '''diameter''' <math>d</math> of a ''k''-tuple is the difference between its largest and smallest elements.<ref name="prob62"/>


==== Definition 2 ====
'''Example''' — the 8-tuple <math>17:\; 0, 2, 6, 12, 14, 20, 24, 26</math> has diameter <math>d = 26</math>.
k-tuple (p + a1, p + a2, p + a3, ..., p + a [k / 2], p + a [k / 2+1], ..., p + a [k-2], p + a [k-1], p + ak) for k even, is called symmetric, if the following condition is satisfied:
a1 + ak = a2 + a[k-1] = a3 + a[k-2] = … = a[k/2] + a[k/2+1]


Example
== Applications ==


symmetric 8-tuple
The project currently runs four CPU-only applications for Windows (x86-64) and Linux (x86-64):<ref name="apps">{{cite web |url=https://boinc.mak.termit.me/odlk2025/apps.php |title=ODLK2025 Applications |accessdate=2026-05-22}}</ref>


(17 + 0, 17 + 2, 17 + 6, 17 + 12, 17 + 14, 17 + 20, 17 + 24, 17 + 26)
{| class="wikitable"
Shortened we write this:
! 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
|}


17: 0, 2, 6, 12, 14, 20, 24, 26
The total average computing power across all applications is approximately '''2,239 GigaFLOPS'''.


==== Definition 3 ====
All applications are CPU-only. GPU support is not currently offered.
k-tuple (p + a1, p + a2, p + a3, ..., p + a [(k-1) / 2], p + a [(k-1) / 2 + 1], p + a [(k-1) / 2 + 2], ..., p + a [k-2], p + a [k-1], p + ak) for k odd called symmetric, if the following condition is satisfied:


a1 + ak = a2 + a[k-1] = a3 +a [k-2] =…= a[(k-1)/2] + a[(k-1)/2+2] = 2 a[(k-1)/2+1]
== Server status (as of 22 May 2026) ==


Example
The following statistics were read directly from the [https://boinc.mak.termit.me/odlk2025/server_status.php project server status page]:<ref name="server_status">{{cite web |url=https://boinc.mak.termit.me/odlk2025/server_status.php |title=ODLK2025 Project Status |accessdate=2026-05-22}}</ref>


symmetric 5-tuple
{| class="wikitable"
18713: 0, 6, 18, 30, 36
! Metric !! Value
(See in [2])
|-
| 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
|}


==== Definition 4 ====
All server daemons (scheduler, feeder, transitioner, validators, assimilators, file deleter) are reported as '''Running'''.
The diameter d of k-tuple is the difference of its largest and smallest elements. [1]
Example
8-tuple


17: 0, 2, 6, 12, 14, 20, 24, 26
== How to participate ==


It has a diameter d = 26.
# Download and install the [https://boinc.berkeley.edu/download.php BOINC client] for your operating system (Windows or Linux).
# In the BOINC Manager, choose '''Add Project''' and enter the URL: <code>https://boinc.mak.termit.me/odlk2025/</code>
# 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 ==
== Project team / Sponsors ==


* Nataliya Makarova, Project scientist
* '''Natalia (Nataliya) Makarova''' — Project scientist; originator of Problem 62 and the underlying algorithms.<ref name="prob62"/>
* termit, Project administrator
* '''termit''' — Project administrator; operates the server infrastructure.
 
== Related projects ==
 
* [https://boinc.termit.me/adsl/ Symmetric Prime Tuples (SPT)] — the parent BOINC project; searches up to <math>2^{64}</math>
* [https://boinc.progger.info/odlk/ ODLK] — earlier project at progger.info hosting related tuple work
* [[wikipedia:PrimeGrid|PrimeGrid]] — a major BOINC project searching for prime numbers of various forms
* [https://gerasim.boinc.ru/ Gerasim@Home] — also runs a "Get Symmetrical Tuples" application using a different algorithm (odd-length tuples only)<ref name="boinc_australia">{{cite web |url=http://forum.boinc-australia.net/index.php?board=223.0 |title=Symmetric Prime Tuples (SPT) — BOINC Australia Forum |accessdate=2026-05-22}}</ref>
 
== Results repository ==
 
Computed results (found tuples) are stored in the project's public database:
 
* [https://boinc.mak.termit.me:5000/ ODLK2025 Results Repository]
 
== Related scientific papers ==
 
* {{cite web |author=Volfson, Victor |title=Dependencies of prime numbers in a tuple |url=https://arxiv.org/pdf/2601.08889 |year=2026 |publisher=arXiv}} — Analyses the Hardy–Littlewood constant for symmetric tuples and proves that it decreases monotonically as tuple length decreases, reflecting weakening inter-prime dependence.
* {{cite web |author=Tóth, László |title=On The Asymptotic Density Of Prime k-tuples and a Conjecture of Hardy and Littlewood |url=https://arxiv.org/abs/1910.02636 |year=2019 |publisher=arXiv}} — Computes "Skewes numbers" for nine prime k-tuples and provides numerical support for the Hardy–Littlewood conjecture.
* {{cite journal |author=Anderson, David P. |title=BOINC: A Platform for Volunteer Computing |journal=Journal of Grid Computing |year=2019 |doi=10.1007/s10723-019-09497-9}} — Describes the BOINC platform on which ODLK2025 runs.
 
== See also ==
 
* [[wikipedia:Prime k-tuple|Prime ''k''-tuple]]
* [[wikipedia:First Hardy–Littlewood conjecture|First Hardy–Littlewood conjecture]]
* [[wikipedia:Berkeley Open Infrastructure for Network Computing|BOINC]]
* [[wikipedia:Volunteer computing|Volunteer computing]]
* [[wikipedia:PrimeGrid|PrimeGrid]]
* [[wikipedia:Twin prime|Twin prime]]
 
== References ==
 
{{Reflist}}
 
== External links ==


* [https://boinc.mak.termit.me/odlk2025/ ODLK2025 official project page]
* [https://boinc.mak.termit.me/odlk2025/server_status.php ODLK2025 server status]
* [https://boinc.mak.termit.me:5000/ Results repository]
* [https://www.primepuzzles.net/problems/prob_062.htm Problem 62: Symmetric k-tuples of consecutive primes] (primepuzzles.net)
* [https://dxdy.ru/topic100750.html Symmetric tuples of consecutive prime numbers] (dxdy.ru forum, in Russian)
* [https://boinc.termit.me/adsl/ Symmetric Prime Tuples (SPT)] — parent BOINC project
* [https://boincsynergy.ca/wiki/ODLK2025/ ODLK2025 on BOINC Synergy]


== Scientific results ==
[[Category:BOINC projects]]
* https://boinc.mak.termit.me/odlk2025/img/results/
[[Category:Distributed computing projects]]
[[Category:Mathematics]]
[[Category:Number theory]]
[[Category:Prime numbers]]
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