SPT: Difference between revisions
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| logo caption = SPT project logo | | logo caption = SPT project logo | ||
| status = | | status = Inactive | ||
| category = Mathematics / Number Theory | | category = Mathematics / Number Theory | ||
| compute = CPU | | compute = CPU | ||
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| sponsor = Natalia Makarova, Alex Belyshev, Tomáš Brada | | sponsor = Natalia Makarova, Alex Belyshev, Tomáš Brada | ||
| maintainer = Natalia Makarova, Alex Belyshev, Tomáš Brada | | maintainer = Natalia Makarova, Alex Belyshev, Tomáš Brada | ||
| released = 2023 | | released = {{Start date and age|2023|06|14}} | ||
| completed = No | |||
| discontinued = {{Start date and age|2025|02|19}} | |||
| programming language = C, C++ | | programming language = C, C++ | ||
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| website = {{URL|https://boinc.termit.me/adsl/}} | | website = {{URL|https://boinc.termit.me/adsl/}} | ||
}} | }} | ||
[https://boinc.termit.me/adsl/ '''''SPT'''''] ('''Symmetric Prime Tuples''') is a [[wikipedia:BOINC|BOINC]]-based [[wikipedia:Volunteer computing|volunteer computing]] project dedicated to researching symmetric [[wikipedia:Prime k-tuple|prime k-tuples]] of consecutive primes, a topic in [[wikipedia:Number theory|number theory]]. Volunteers donate idle CPU time on their personal computers to help systematically search for symmetric prime k-tuples, advancing an open mathematical problem first formally presented by mathematician Natalia Makarova. The project is hosted at <code>boinc.termit.me/adsl/</code> and serves as the direct continuation of an earlier lineage of BOINC projects pursuing the same mathematical goal. | [https://boinc.termit.me/adsl/ '''''SPT'''''] ('''Symmetric Prime Tuples''') is a [[wikipedia:BOINC|BOINC]]-based [[wikipedia:Volunteer computing|volunteer computing]] project dedicated to researching symmetric [[wikipedia:Prime k-tuple|prime k-tuples]] of consecutive primes, a topic in [[wikipedia:Number theory|number theory]]. Volunteers donate idle CPU time on their personal computers to help systematically search for symmetric prime k-tuples, advancing an open mathematical problem first formally presented by mathematician Natalia Makarova. The project is hosted at <code>boinc.termit.me/adsl/</code> and serves as the direct continuation of an earlier lineage of BOINC projects pursuing the same mathematical goal. | ||
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== Background and History == | == Background and History == | ||
[[File:Ulam 1.png|thumb| | [[File:Ulam 1.png|thumb|296x296px|The [[wikipedia:Ulam spiral|Ulam spiral]], a visualisation of the distribution of prime numbers. SPT investigates a specific structural property of consecutive primes: whether they can be arranged in symmetric patterns.]] | ||
The search for symmetric prime tuples has a rich history within the volunteer computing community. The research lineage traces back to '''Stop@Home''', an early BOINC project that searched for symmetric prime sequences.<ref>{{cite web |url=http://www.primepuzzles.net/problems/prob_062.htm |title=Problem 62. Symmetric k-tuples of consecutive primes |publisher=primepuzzles.net |access-date=2026-05-23}}</ref> Stop@Home achieved a notable result: in April 2017, the project's volunteers discovered a minimal symmetric 17-tuple with starting prime <math>p = 159{,}067{,}808{,}851{,}610{,}411</math> and offsets 0, 42, 60, 96, 102, 186, 210, 240, 246, 252, 282, 306, 390, 396, 432, 450, 492.<ref>{{cite web |url=http://www.primepuzzles.net/problems/prob_062.htm |title=Problem 62. Symmetric k-tuples of consecutive primes |publisher=primepuzzles.net |access-date=2026-05-23}}</ref> | The search for symmetric prime tuples has a rich history within the volunteer computing community. The research lineage traces back to '''Stop@Home''', an early BOINC project that searched for symmetric prime sequences.<ref>{{cite web |url=http://www.primepuzzles.net/problems/prob_062.htm |title=Problem 62. Symmetric k-tuples of consecutive primes |publisher=primepuzzles.net |access-date=2026-05-23}}</ref> Stop@Home achieved a notable result: in April 2017, the project's volunteers discovered a minimal symmetric 17-tuple with starting prime <math>p = 159{,}067{,}808{,}851{,}610{,}411</math> and offsets 0, 42, 60, 96, 102, 186, 210, 240, 246, 252, 282, 306, 390, 396, 432, 450, 492.<ref>{{cite web |url=http://www.primepuzzles.net/problems/prob_062.htm |title=Problem 62. Symmetric k-tuples of consecutive primes |publisher=primepuzzles.net |access-date=2026-05-23}}</ref> | ||
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=== Definition 4: Diameter === | === Definition 4: Diameter === | ||
[[File:BOINC logo.png|right|frameless|150x150px|BOINC, the Berkeley Open Infrastructure for Network Computing, is the platform that powers SPT.]] | |||
The '''diameter''' <math>d</math> of a k-tuple is the difference between its largest and smallest offsets:<ref>{{cite web |url=http://oeis.org/A055380 |title=OEIS A055380 |publisher=The OEIS Foundation |access-date=2026-05-23}}</ref> | The '''diameter''' <math>d</math> of a k-tuple is the difference between its largest and smallest offsets:<ref>{{cite web |url=http://oeis.org/A055380 |title=OEIS A055380 |publisher=The OEIS Foundation |access-date=2026-05-23}}</ref> | ||
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== Known Solutions == | == Known Solutions == | ||
[[File:Sieve of Eratosthenes animation.gif|thumb| | [[File:Sieve of Eratosthenes animation.gif|thumb|296x296px|The [[wikipedia:Sieve of Eratosthenes|Sieve of Eratosthenes]], the classical prime-finding algorithm underlying the modern primesieve library used by SPT.]] | ||
The table below summarises the best known solutions for various values of <math>k</math>, as published on the project's reference page.<ref>{{cite web |url=http://www.primepuzzles.net/problems/prob_062.htm |title=Problem 62. Symmetric k-tuples of consecutive primes |publisher=primepuzzles.net |access-date=2026-05-23}}</ref> Solutions marked "not minimal" indicate that a smaller starting prime <math>p</math> or smaller diameter may still exist. Results were discovered across Stop@Home, TBEG, manual computation by contributors such as J. Wroblewski and two anonymous Russian contributors, and the ongoing SPT project. | The table below summarises the best known solutions for various values of <math>k</math>, as published on the project's reference page.<ref>{{cite web |url=http://www.primepuzzles.net/problems/prob_062.htm |title=Problem 62. Symmetric k-tuples of consecutive primes |publisher=primepuzzles.net |access-date=2026-05-23}}</ref> Solutions marked "not minimal" indicate that a smaller starting prime <math>p</math> or smaller diameter may still exist. Results were discovered across Stop@Home, TBEG, manual computation by contributors such as J. Wroblewski and two anonymous Russian contributors, and the ongoing SPT project. | ||