ODLK2025: Difference between revisions
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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> | <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> | ||
[[File:{{#setmainimage:Odlk2025. | [[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 ... | ||
== Why ODLK2025? == | == Why ODLK2025? == | ||
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== Goal == | == Goal == | ||
The project solves the problem of finding symmetric tuples of consecutive prime numbers, | 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. | ||
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 | In particular, the problem of finding symmetric tuples of length 17 of consecutive prime numbers according to the following pattern | ||
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 | 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 | 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. | ||
tuple of length 19 of consecutive prime numbers with a minimum diameter of 252. | |||
Currently, this subproblem is being solved in a non-BOINC project | Currently, this subproblem is being solved in a non-BOINC project | ||
https://boinc.termit.me/adsl/forum_thread.php?id=79 | https://boinc.termit.me/adsl/forum_thread.php?id=79 | ||
https://boinc.progger.info/odlk/forum_thread.php?id=293 | https://boinc.progger.info/odlk/forum_thread.php?id=293 | ||
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 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. | ||
See the topic "Symmetric tuples of consecutive prime numbers" | |||
https://dxdy.ru/topic100750.html | See the topic "Symmetric tuples of consecutive prime numbers" https://dxdy.ru/topic100750.html | ||
== Methods == | == Methods == | ||
Definition 1 | |||
==== 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), | ||
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. [1] | ||
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: | ||
a1 + ak = a2 + a[k-1] = a3 + a[k-2] = … = a[k/2] + a[k/2+1] | a1 + ak = a2 + a[k-1] = a3 + a[k-2] = … = a[k/2] + a[k/2+1] | ||
Example | Example | ||
symmetric 8-tuple | symmetric 8-tuple | ||
(17 + 0, 17 + 2, 17 + 6, 17 + 12, 17 + 14, 17 + 20, 17 + 24, 17 + 26) | (17 + 0, 17 + 2, 17 + 6, 17 + 12, 17 + 14, 17 + 20, 17 + 24, 17 + 26) | ||
Shortened we write this: | Shortened we write this: | ||
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: | ||
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] | 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] | ||
Example | Example | ||
symmetric 5-tuple | symmetric 5-tuple | ||
18713: 0, 6, 18, 30, 36 | 18713: 0, 6, 18, 30, 36 | ||
(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] | ||
Example | Example | ||
8-tuple | 8-tuple | ||
17: 0, 2, 6, 12, 14, 20, 24, 26 | 17: 0, 2, 6, 12, 14, 20, 24, 26 | ||
It has a diameter d = 26. | It has a diameter d = 26. | ||