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Distributed computing project
Open to all forum users and guests, who have the opportunity to use their computing resources.
We are looking for:
1. Smallest number such that there are n symmetric (in the gap sense) primes on each side.
http://oeis.org/A055381Result are found for n = 22:
633925574060671: 0 16 40 48 58 112 118 148 156 198 216 232 250 292 300 330 336 390 400 408 432 448(author Dmitry Petukhov)
Now we need to find the following solution: for n = 24.
2. Central prime p in the smallest (2n+1)-tuple of consecutive primes that are symmetric with respect to p.
http://oeis.org/A055380
and
a(n) = the smallest prime p(k) such that p(k+j) – p(k+j-1) = p(n+k+1-j) – p(n+k-j) for all j with 1 <= j <= n.
http://oeis.org/A175309Result are found for n = 15:
3945769040698829: 0 12 18 42 102 138 180 210 240 282 318 378 402 408 420(author Dmitry Petukhov)
Now we need to find the following solution: for n = 17.
3. Sequence of paragraph 1 for n = 16
such that the sequence of the numbers, you can make pandiagonal square of order 4.Found the following results:
a)
170693941183817: 0 30 42 44 72 74 86 90 116 120 132 134 162 164 176 206(author Max Alexeyev; see
The set of 16 consecutive primes forming a 4×4 pandiagonal magic square with the smallest magic constant (682775764735680).
http://oeis.org/A245721)b)
11796223202765101: 0 22 36 58 90 112 126 148 210 232 246 268 300 322 336 358
(author Dmitry Petukhov)c)
17537780902038437: 0 6 60 66 126 132 144 150 186 192 204 210 270 276 330 336
(author Dmitry Petukhov)The program for project (author Alex Belyshev)
You can write a program to find solutions.
And you can use a program made specifically for this project:
https://yadi.sk/d/rJkoP5N-d83ebAuthor of the program wrote about it here
http://dxdy.ru/post939664.html#p939664This program allows you to search for the natural numbers up to 1.8*10^18.
Participants of the project
1. Natalia Makarova (author of the project)
2. Alex Belyshev (author of the program)
3. Max Alekseyev
4. Dmitry PetukhovLinks
http://dxdy.ru/post939431.html#p939431
http://dxdy.ru/post938945.html#p938945
http://dxdy.ru/post891839.html#p891839
http://dxdy.ru/post973283.html#p973283
http://dxdy.ru/post974234.html#p974234
http://dxdy.ru/post939603.html#p939603Contact
[email protected]Note
Known solution to paragraph 3, found earlier:
d)
320572022166380833: 0 6 10 16 18 24 28 34 60 66 70 76 78 84 88 94(authors J. Wroblewski and J.K. Andersen, see
http://www.primepuzzles.net/conjectures/conj_042.htm )The new solution to paragraph 3
e) author D. Petukhov
12548708437706431: 0 12 18 28 30 40 46 58 210 222 228 238 240 250 256 268The new solutions to paragraph 3, author D. Petukhov:
17537780902038437: 0 6 60 66 126 132 144 150 186 192 204 210 270 276 330 336 19171351137406219: 0 22 30 48 52 70 78 90 100 112 120 138 142 160 168 190See
http://dxdy.ru/post988507.html#p988507
http://dxdy.ru/post995245.html#p995245
http://oeis.org/A256234The new solutions to paragraph 3:
23323776496051501: 0 30 42 66 72 96 100 108 130 138 142 166 172 196 208 238 23653934725904299: 0 12 22 34 48 60 70 82 90 102 112 124 138 150 160 172See http://dxdy.ru/post1035485.html#p1035485
The new solution to paragraph 1 (n=24):
22930603692243271: 0 70 76 118 136 156 160 178 202 222 238 250 378 390 406 426 450 468 472 492 510 552 558 628There is a new program for for this project from Alex Belyshev
https://yadi.sk/d/a0l3LOCAhphqWTo run the program, need write in the file start.txt beginning of interval, for example:
28000000000000000.Now run the program kpppch_16_do_33.exe
The program works like this:
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