SPT - Revision history

Al Piskun at 13:48, 21 July 2026

2026-07-21T13:48:17Z

← Older revision		Revision as of 13:48, 21 July 2026
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	== Known Solutions ==		== Known Solutions ==

	[[File:Sieve of Eratosthenes animation.gif\|thumb\|~~right\|220px~~\|The [[wikipedia:Sieve of Eratosthenes\|Sieve of Eratosthenes]], the classical prime-finding algorithm underlying the modern primesieve library used by SPT.]]		[[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.

Al Piskun: edit status

2026-07-21T13:47:01Z

edit status

← Older revision		Revision as of 13:47, 21 July 2026
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	\| logo caption = SPT project logo		\| logo caption = SPT project logo

	\| status = ~~Active~~		\| 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/}}
	}}		}}

	~~[[File:BOINC logo.png\|right\|frameless\|150x150px\|BOINC, the Berkeley Open Infrastructure for Network Computing, is the platform that powers SPT.]]~~

	[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\|~~right\|220px~~\|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.]]		[[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>

Al Piskun: update and infobox

2026-05-24T03:57:06Z

update and infobox

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Al Piskun: update and add infobox

2026-05-23T11:21:32Z

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Al Piskun: /* Methods */ add links

2024-04-07T12:03:04Z

Methods: add links

← Older revision		Revision as of 12:03, 7 April 2024
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	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 (p + a1, p + a2, p + a3, …, p + ak),

	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]		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. [https://en.wikipedia.org/wiki/Prime_k-tuple]

	We consider the k-tuple, where p + a1, p + a2, p + a3, ..., p + ak are consecutive primes.		We consider the k-tuple, where p + a1, p + a2, p + a3, ..., p + ak are consecutive primes.
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	'''''Definition 4'''''		'''''Definition 4'''''

	The diameter d of k-tuple is the difference of its largest and smallest elements. [1]		The diameter d of k-tuple is the difference of its largest and smallest elements.[http://oeis.org/A055380]

	Example		Example
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	It has a diameter d = 26.		It has a diameter d = 26.

	Known solutions with a minimal diameter and a minimal value of p for k = 2, 4, 6, 8 see in [1]		Known solutions with a minimal diameter and a minimal value of p for k = 2, 4, 6, 8 see in [http://oeis.org/A081235]

	Further,		Further,

Al Piskun: /* Methods */ wording

2024-04-07T11:39:33Z

Methods: wording

← Older revision		Revision as of 11:39, 7 April 2024
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	The search code itself (in SPT), according to the constructed matrix, takes up only 5-6MB in memory. And it doesn't increase.		The search code itself (in SPT), according to the constructed matrix, takes up only 5-6MB in memory. And it doesn't increase.

	When the project started, the memory size for the matrix of one task was approximately 620MB. The memory size is now 1.3 GB and will slowly increase. The longer the numbers, the more memory they require in the primesieve matrix. One ~~of our tasks~~ takes, on average, from 45 minutes to 1.5 hours, although there are exceptions to this rule. There are cruncher computers that ~~count~~ in 20 minutes and also computers that ~~count~~ in 240 minutes.[https://boinc.termit.me/adsl/faq-en.php]		When the project started, the memory size for the matrix of one task was approximately 620MB. The memory size is now 1.3 GB and will slowly increase. The longer the numbers, the more memory they require in the primesieve matrix. One task takes, on average, from 45 minutes to 1.5 hours, although there are exceptions to this rule. There are cruncher computers that complete a work unit in 20 minutes and also computers that complete in 240 minutes.[https://boinc.termit.me/adsl/faq-en.php]

	The SPT application is based on '''''[http://www.primepuzzles.net/problems/prob_062.htm Problem 62. Symmetric k-tuples of consecutive primes]''''' presented by Natalia Makarova.		The SPT application is based on '''''[http://www.primepuzzles.net/problems/prob_062.htm Problem 62. Symmetric k-tuples of consecutive primes]''''' presented by Natalia Makarova.

Al Piskun: /* Methods */remove whitespace

2024-04-07T11:36:55Z

Methods: remove whitespace

← Older revision		Revision as of 11:36, 7 April 2024
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	The search code itself (in SPT), according to the constructed matrix, takes up only 5-6MB in memory. And it doesn't increase.		The search code itself (in SPT), according to the constructed matrix, takes up only 5-6MB in memory. And it doesn't increase.

	When the project started, the memory size for the matrix of one task was approximately 620MB. The memory size is now 1.3 GB and will slowly increase.		When the project started, the memory size for the matrix of one task was approximately 620MB. The memory size is now 1.3 GB and will slowly increase. The longer the numbers, the more memory they require in the primesieve matrix. One of our tasks takes, on average, from 45 minutes to 1.5 hours, although there are exceptions to this rule. There are cruncher computers that count in 20 minutes and also computers that count in 240 minutes.[https://boinc.termit.me/adsl/faq-en.php]

	The longer the numbers, the more memory they require in the primesieve matrix.

	One of our tasks takes, on average, from 45 minutes to 1.5 hours, although there are exceptions to this rule.

	There are cruncher computers that count in 20 minutes and also computers that count in 240 minutes.[https://boinc.termit.me/adsl/faq-en.php]

	The SPT application is based on '''''[http://www.primepuzzles.net/problems/prob_062.htm Problem 62. Symmetric k-tuples of consecutive primes]''''' presented by Natalia Makarova.		The SPT application is based on '''''[http://www.primepuzzles.net/problems/prob_062.htm Problem 62. Symmetric k-tuples of consecutive primes]''''' presented by Natalia Makarova.

Al Piskun: /* Methods */ update

2024-04-07T11:20:45Z

Methods: update

← Older revision		Revision as of 11:20, 7 April 2024
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	== Methods ==		== Methods ==
	~~The~~ SPT ~~code~~ is ~~published here: '''''https://github~~.~~com/DemIS-1/spt'''''~~		Currently the SPT application takes up about 1.3 GB of RAM in the computer memory. 99% of this 1.3 GB is taken up by constructing a matrix of prime numbers.

	'''Definition 1'''		The matrix of prime numbers is made by the code primesieve. Specific code snippet: '''''https://github.com/kimwalisch/primesieve/tree/2b2c4a5c62f0cd9dfd9f56cca580ea47fa84dc2d'''''

			Original sources from Tomash Brada: '''''https://github.com/tomasbrod/tbboinc/tree/primes/symprtu'''''

			Adapted by Demis for SPT project: '''''https://github.com/DemIS-1/spt'''''

			The search code itself (in SPT), according to the constructed matrix, takes up only 5-6MB in memory. And it doesn't increase.

			When the project started, the memory size for the matrix of one task was approximately 620MB. The memory size is now 1.3 GB and will slowly increase.

			The longer the numbers, the more memory they require in the primesieve matrix.

			One of our tasks takes, on average, from 45 minutes to 1.5 hours, although there are exceptions to this rule.

			There are cruncher computers that count in 20 minutes and also computers that count in 240 minutes.[https://boinc.termit.me/adsl/faq-en.php]

			The SPT application is based on '''''[http://www.primepuzzles.net/problems/prob_062.htm Problem 62. Symmetric k-tuples of consecutive primes]''''' presented by Natalia Makarova.

			'''''Definition 1'''''

	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 (p + a1, p + a2, p + a3, …, p + ak),
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	We consider the k-tuple, where p + a1, p + a2, p + a3, ..., p + ak are consecutive primes.		We consider the k-tuple, where p + a1, p + a2, p + a3, ..., p + ak are consecutive primes.

	'''Definition 2'''		'''''Definition 2'''''

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

	'''Definition 3'''		'''''Definition 3'''''

	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:		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:
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	(See in [2])		(See in [2])

	'''Definition 4'''		'''''Definition 4'''''

	The diameter d of k-tuple is the difference of its largest and smallest elements. [1]		The diameter d of k-tuple is the difference of its largest and smallest elements. [1]
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	For k = 17, 19, 21, 23 solutions no found.		For k = 17, 19, 21, 23 solutions no found.

	'''Questions'''		'''''Questions'''''

	1. Find solutions with a minimal diameter and a minimal value of p for 10 < k < 17, k = 18, 20, 22, 24.		1. Find solutions with a minimal diameter and a minimal value of p for 10 < k < 17, k = 18, 20, 22, 24.

	2. Find solutions for the remaining k, minimal or not minimal.		2. Find solutions for the remaining k, minimal or not minimal.

	~~'''''[http://www.primepuzzles.net/problems/prob_062.htm Problem 62. Symmetric k-tuples of consecutive primes].'''''~~

	== Project team ==		== Project team ==
	Natalia Makarova. Alex Belyshev. Tomáš Brada.		Demis. Natalia Makarova. Alex Belyshev. Tomáš Brada.

	== Scientific results ==		== Scientific results ==
	Results of this project are available in the '''''[https://boinc.tbrada.eu/spt/explore.php Prime Tuple Database].'''''		Results of this project are available in the '''''[https://boinc.tbrada.eu/spt/explore.php Prime Tuple Database].'''''

Al Piskun at 18:28, 2 April 2024

2024-04-02T18:28:37Z

← Older revision		Revision as of 18:28, 2 April 2024
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	== Methods ==		== Methods ==
			The SPT code is published here: '''''https://github.com/DemIS-1/spt'''''

	'''Definition 1'''		'''Definition 1'''

Al Piskun: Methods/ details

2024-03-17T20:16:51Z

Methods/ details

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