Result will be published after the ending of competition
Archivi categoria: K-Tuple
Ranking for K-Tuples of Primes (2)
The solution on the competition are checked by hand, so there is no a real-time ranking when one submit an entry.
|
Pos
|
User
|
Date
|
Task
|
|---|---|---|---|
|
1
|
Natalia Makarova
|
02/01/2024
|
4
|
|
2
|
Natalia Makarova
|
04/01/2024
|
2
|
Primes k-tuple (2)
Competition #5
This competition is organized by Макарова Наталия (Natalia Makarova)
Introduction
Basic definitions of k-tuples primes can be found in [1] and [3].
Definition 1:
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.
Definition 2:
The diameter d of k-tuple is the difference of its largest and smallest elements.
We are considering k-tuples of consecutive primes, so
p + a1, p + a2, p + a3, …, p + ak
are sequential prime numbers.
We consider symmetric k-tuples.
See Definition 2 and Definition 3 in [3].
Definition 3:
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]
Definition 4:
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]
We write the k-tuple pattern this way
0, p_2, p_3, …, p_k
where p_k are even numbers.
For example, a pattern for 17-tuple
0, 6, 24, 36, 66, 84, 90, 114, 120, 126, 150, 156, 174, 204, 216, 234, 240
We write the k-tuple this way
X: 0, p_2, p_3, …, p_k
where X is a prime number.
For example, 17-tuple (author J. Wroblewski)
1006882292528806742267: 0, 6, 24, 36, 66, 84, 90, 114, 120, 126, 150, 156, 174, 204, 216, 234, 240
The most difficult task is to find the minimum k-tuple with the minimum diameter d.
In such a k-tuple, for the minimum value of d, the value of X is the minimum.
For example, a minimum 17-tuple with a minimum diameter of 240 (author J. Wroblewski)
258406392900394343851: 0, 12, 30, 42, 60, 72, 78, 102, 120, 138, 162, 168, 180, 198, 210, 228, 240
d = 240 (minimum)
X = 258406392900394343851 (minimum)
For the competition there are 7 tasks that you can compete.
Tasks
Task #1
Search 17-tuple with pattern
0, 6, 24, 36, 66, 84, 90, 114, 120, 126, 150, 156, 174, 204, 216, 234, 240
Currently there are 8 known solutions (authors J. Wroblewski and D. Petukhov)
1006882292528806742267: 0 6 24 36 66 84 90 114 120 126 150 156 174 204 216 234 240 3954328349097827424397: 0 6 24 36 66 84 90 114 120 126 150 156 174 204 216 234 240 4896552110116770789773: 0 6 24 36 66 84 90 114 120 126 150 156 174 204 216 234 240 6751407944109046348063: 0 6 24 36 66 84 90 114 120 126 150 156 174 204 216 234 240 7768326730875185894807: 0 6 24 36 66 84 90 114 120 126 150 156 174 204 216 234 240 19252814175273852997757: 0 6 24 36 66 84 90 114 120 126 150 156 174 204 216 234 240 154787380396512840656507: 0 6 24 36 66 84 90 114 120 126 150 156 174 204 216 234 240 901985248981556228168767: 0 6 24 36 66 84 90 114 120 126 150 156 174 204 216 234 240
We do not guarantee that there are no missing solutions in this list.
It is required to find missing solutions, if they exist.
And you also need to continue the list of solutions, that is, find solutions for X > 901985248981556228168767.
See [7].
Task #2
Currently two 19-tuples are known
6919940122097246303: 0, 48, 78, 138, 198, 204, 210, 264, 288, 294, 300, 324, 378, 384, 390, 450, 510, 540, 588 7325015925425379457: 0, 6, 30, 90, 126, 132, 150, 162, 216, 246, 276, 330, 342, 360, 366, 402, 462, 486, 492
Solutions found in the BOINC project SPT. [9]
It is not known whether the first solution is minimal.
We need to find the minimum solution, if it exists.
The diameter can be any.
In other words, we need to find a solution
Х: 0, p_2, p_3, …, p_17, p_18, p_19
for X < 6919940122097246303
if such a solution exists.
See [6].
Task #3
You need to find a 19-tuple with a minimum diameter d = 252
Х: 0, 6, 12, 30, 42, 72, 90, 96, 120, 126, 132, 156, 162, 180, 210, 222, 240, 246, 252
If you guarantee that X is minimal, that’s good, but that condition doesn’t have to be true.
So far we do not know any solution for this task.
Task #1 can help you complete this task.
See [7] and [10].
Task #4
Two 18-tuples with a minimum diameter d = 82 are known (author J. Wroblewski)
824871967574850703732309: 0, 4, 10, 12, 18, 22, 28, 30, 40, 42, 52, 54, 60, 64, 70, 72, 78, 82 2124773992554613163708029: 0, 4, 10, 12, 18, 22, 28, 30, 40, 42, 52, 54, 60, 64, 70, 72, 78, 82
It is not known whether the first solution is minimal.
Need to find 18-tuple
Х: 0, 4, 10, 12, 18, 22, 28, 30, 40, 42, 52, 54, 60, 64, 70, 72, 78, 82
for X < 824871967574850703732309, if such a solution exists.
See [11] and [12].
Task #5
Known 20-tuple with a minimum diameter d = 94 (authors N. Makarova and J. Wroblewski)
824871967574850703732303: 0, 6, 10, 16, 18, 24, 28, 34, 36, 46, 48, 58, 60, 66, 70, 76, 78, 84, 88, 94
It is unknown whether this solution is minimal.
We need to find the minimum solution, if it exists.
Theoretical patterns for 20-tuple with minimum diameter
0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 60, 64, 66, 70, 76, 78, 84, 88, 90, 94 0, 4, 6, 10, 16, 18, 24, 28, 34, 36, 58, 60, 66, 70, 76, 78, 84, 88, 90, 94 0, 4, 6, 10, 16, 18, 24, 28, 36, 46, 48, 58, 66, 70, 76, 78, 84, 88, 90, 94 0, 4, 6, 10, 16, 18, 24, 30, 34, 46, 48, 60, 64, 70, 76, 78, 84, 88, 90, 94 0, 4, 6, 10, 16, 18, 24, 34, 36, 46, 48, 58, 60, 70, 76, 78, 84, 88, 90, 94 0, 6, 10, 16, 18, 24, 28, 34, 36, 46, 48, 58, 60, 66, 70, 76, 78, 84, 88, 94
See [12], [13] and [15].
Task #6
Currently two 26-tuples are known
5179852391836338871: 0, 12, 18, 28, 46, 76, 78, 120, 186, 210, 226, 232, 238, 300, 306, 312, 328, 352, 418, 460, 462, 492, 510, 520, 526, 538 7331618973503379271: 0, 22, 30, 36, 40, 52, 58, 72, 120, 160, 190, 192, 220, 348, 376, 378, 408, 448, 496, 510, 516, 528, 532, 538, 546, 568
Solutions found in the BOINC project SPT. [9]
It is not known whether the first solution is minimal.
Need to find 26-tuple
Х: 0, p_2, p_3, …, p_24, p_25, p_26
for X < 5179852391836338871, if such a solution exists.
See [9].
Task #7
Need to find 21-tuple
Х: 0, p_2, p_3, …, p_19, p_20, p_21
for any X and for any diameter d.
For minimum d = 324 there are two theoretical patterns
0, 12, 30, 42, 54, 60, 72, 84, 114, 120, 162, 204, 210, 240, 252, 264, 270, 282, 294, 312, 324 0, 12, 30, 42, 54, 60, 84, 114, 120, 144, 162, 180, 204, 210, 240, 264, 270, 282, 294, 312, 324
See [14] and [15].
Rules
You can complete one or more of the seven suggested tasks.
You can use the algorithms and programs that you will find at the links below.
You are allowed to use any computer technology, including clusters and supercomputers.
When you send a solution in the submit entry page, to help as in verify it, please enter a tuple in this format:
T# X: 0, p_2, p_3, …, p_k
Where T is the task number and the rest is the k-tuple in standard format in a new line.
Organizational matters
The competition begins on January 4, 2024 and will last six months (ending on July 4, 2024).
Solutions found during the competition will not be published until the end of the competition.
Solutions must be entered in the specified format only (see Rules).
Solutions will be checked by the competition organizers.
The winner of the competition will receive a prize of 10,000 RUR.
For a foreign winner, the amount will be converted into US dollars at the Russian exchange rate on the day the competition ends.
The winner will be determined by the competition organizers based on the totality of submitted solutions.
Organizers
Natalia Makarova
contact [email protected]
Stefano Tognon
contact [email protected]
Links
- Prime k-tuple
https://en.wikipedia.org/wiki/Prime_k-tuple - Problem 60. Symmetric primes on each side.
http://www.primepuzzles.net/problems/prob_060.htm - Problem 62. Symmetric k-tuples of consecutive primes
http://www.primepuzzles.net/problems/prob_062.htm - Smallest prime starting a sequence of 2n consecutive odd primes with symmetrical gaps about the center.
https://oeis.org/A055382 - Symmetric tuples of sequential primes in OEIS
https://boinc.progger.info/odlk/forum_thread.php?id=259 - Central prime p in the smallest (2n+1)-tuple of consecutive primes that are symmetric with respect to p.
https://oeis.org/A055380 - Development of a new algorithm
https://boinc.progger.info/odlk/forum_thread.php?id=268 - Symmetric tuples of sequential primes
https://dxdy.ru/topic100750.html - BOINC-project SPT
https://boinc.termit.me/adsl/ - Symmetric tuple of length 19 with minimum diameter of consecutive primes
https://boinc.progger.info/odlk/forum_thread.php?id=269 - Minimization problem 18-tuple with minimum diameter
https://boinc.progger.info/odlk/forum_thread.php?id=266 - Smallest prime starting a (nonsingular) symmetric n-tuplet of the shortest span (=A266511(n)).
https://oeis.org/A266512 - Minimization problem 20-tuple with minimum diameter
https://boinc.progger.info/odlk/forum_thread.php?id=267 - Symmetric tuple of length 21 with minimum diameter of consecutive primes
https://boinc.progger.info/odlk/forum_thread.php?id=270 - Natalia Makarova and Vladimir Chirkov, Theoretical patterns with a minimal diameter for a(2) – a(50)
https://oeis.org/A266512/a266512_1.txt
Result for K-Tuples of Primes
The competition K-Tuples of Primes is over.
Thanks to all people that have partecipate.
The winner is Jarek (see Ranking)
The result is in this table:
|
Task
|
K-tuple
|
Diameter
|
Prime
|
Magic(*)
|
Name
|
|---|---|---|---|---|---|
|
1
|
17
|
240
|
1006882292528806742267
|
0
|
Jarek
|
|
0,6,24,36,66,84,90,114,120,126,150,156,174,204,216,234,240
|
|||||
|
1
|
17
|
348
|
11954696436290948869
|
0
|
Jarek
|
|
0,18,60,78,90,138,144,168,174,180,204,210,258,270,288,330,348
|
|||||
|
1
|
17
|
360
|
12196464604998841777
|
0
|
Jarek
|
|
0,36,84,96,114,120,126,150,180,210,234,240,246,264,276,324,360
|
|||||
|
1
|
17
|
264
|
1338977422865229706499
|
0
|
Jarek
|
|
0,12,24,30,42,54,84,90,132,174,180,210,222,234,240,252,264
|
|||||
|
1
|
17
|
360
|
14271237683005753507
|
0
|
Jarek
|
|
0,24,30,84,96,114,150,156,180,204,210,246,264,276,330,336,360
|
|||||
|
1
|
17
|
348
|
17667344133365404873
|
0
|
Jarek
|
|
0,30,48,84,90,108,114,150,174,198,234,240,258,264,300,318,348
|
|||||
|
1
|
17
|
420
|
18462005826764715791
|
0
|
Jarek
|
|
0,78,90,102,120,162,168,192,210,228,252,258,300,318,330,342,420
|
|||||
|
1
|
17
|
240
|
19252814175273852997757
|
0
|
Jarek
|
|
0,6,24,36,66,84,90,114,120,126,150,156,174,204,216,234,240
|
|||||
|
1
|
17
|
240
|
20278587540464136529199
|
0
|
Jarek
|
|
0,12,30,42,60,72,78,102,120,138,162,168,180,198,210,228,240
|
|||||
|
1
|
17
|
264
|
2035559077035293441299
|
0
|
Jarek
|
|
0,12,24,42,54,84,90,114,132,150,174,180,210,222,240,252,264
|
|||||
|
1
|
17
|
240
|
24300494153317939112651
|
0
|
Jarek
|
|
0,12,18,30,42,72,78,102,120,138,162,168,198,210,222,228,240
|
|||||
|
1
|
17
|
240
|
25651315879379564172971
|
0
|
Jarek
|
|
0,12,18,30,42,72,78,102,120,138,162,168,198,210,222,228,240
|
|||||
|
1
|
17
|
240
|
258406392900394343851
|
0
|
Jarek
|
|
0,12,30,42,60,72,78,102,120,138,162,168,180,198,210,228,240
|
|||||
|
1
|
17
|
288
|
311634572279873026493
|
0
|
Jarek
|
|
0,18,54,60,78,84,120,138,144,150,168,204,210,228,234,270,288
|
|||||
|
1
|
17
|
240
|
32686971428909208943211
|
0
|
Jarek
|
|
0,12,30,42,60,72,78,102,120,138,162,168,180,198,210,228,240
|
|||||
|
1
|
17
|
264
|
384703558068522780559
|
0
|
Jarek
|
|
0,24,30,42,72,84,90,114,132,150,174,180,192,222,234,240,264
|
|||||
|
1
|
17
|
240
|
3954328349097827424397
|
0
|
Jarek
|
|
0,6,24,36,66,84,90,114,120,126,150,156,174,204,216,234,240
|
|||||
|
1
|
17
|
252
|
401276622469261903031
|
0
|
Jarek
|
|
0,6,12,30,72,90,96,120,126,132,156,162,180,222,240,246,252
|
|||||
|
1
|
17
|
324
|
443707110791502007579
|
0
|
Jarek
|
|
0,42,72,84,114,120,132,150,162,174,192,204,210,240,252,282,324
|
|||||
|
1
|
17
|
240
|
4896552110116770789773
|
0
|
Jarek
|
|
0,6,24,36,66,84,90,114,120,126,150,156,174,204,216,234,240
|
|||||
|
1
|
17
|
288
|
535010601740877140023
|
0
|
Jarek
|
|
0,18,54,60,78,84,120,138,144,150,168,204,210,228,234,270,288
|
|||||
|
1
|
17
|
252
|
568398209014995678701
|
0
|
Jarek
|
|
0,6,12,30,42,72,90,96,126,156,162,180,210,222,240,246,252
|
|||||
|
1
|
17
|
240
|
6751407944109046348063
|
0
|
Jarek
|
|
0,6,24,36,66,84,90,114,120,126,150,156,174,204,216,234,240
|
|||||
|
1
|
17
|
312
|
6837359459759035391
|
0
|
Jarek
|
|
0,42,60,66,72,120,126,150,156,162,186,192,240,246,252,270,312
|
|||||
|
1
|
17
|
444
|
702939111495760681807
|
0
|
Jarek
|
|
0,90,102,132,144,174,180,210,222,234,264,270,300,312,342,354,444
|
|||||
|
1
|
17
|
252
|
752853880537802642981
|
0
|
Jarek
|
|
0,6,12,30,42,72,96,120,126,132,156,180,210,222,240,246,252
|
|||||
|
1
|
17
|
240
|
7768326730875185894807
|
0
|
Jarek
|
|
0,6,24,36,66,84,90,114,120,126,150,156,174,204,216,234,240
|
|||||
|
1
|
17
|
360
|
7902083290948579129
|
0
|
Jarek
|
|
0,12,18,102,132,138,150,168,180,192,210,222,228,258,342,348,360
|
|||||
|
1
|
17
|
360
|
8053379680763235601
|
0
|
Jarek
|
|
0,18,48,60,102,132,138,150,180,210,222,228,258,300,312,342,360
|
|||||
|
2
|
14
|
56
|
10421030292115097
|
0
|
Natalia Makarova
|
|
0, 2, 6, 12, 14, 20, 26, 30, 36, 42, 44, 50, 54, 56
|
|||||
|
2
|
17
|
240
|
258406392900394343851
|
0
|
Jarek
|
|
0,12,30,42,60,72,78,102,120,138,162,168,180,198,210,228,240
|
|||||
|
2
|
15
|
180
|
3112462738414697093
|
0
|
Jarek
|
|
0,6,24,30,54,66,84,90,96,114,126,150,156,174,180
|
|||||
|
2
|
12
|
46
|
41280160361347
|
0
|
Natalia Makarova
|
|
0, 4, 6, 10, 12, 22, 24, 34, 36, 40, 42, 46
|
|||||
|
2
|
20
|
94
|
824871967574850703732303
|
0
|
Jarek
|
|
0,6,10,16,18,24,28,34,36,46,48,58,60,66,70,76,78,84,88,94
|
|||||
|
2
|
20
|
94
|
824871967574850703732303
|
0
|
Natalia Makarova
|
|
0, 6, 10, 16, 18, 24, 28, 34, 36, 46, 48, 58, 60, 66, 70, 76, 78, 84, 88, 94
|
|||||
|
2
|
18
|
82
|
824871967574850703732309
|
0
|
Jarek
|
|
0,4,10,12,18,22,28,30,40,42,52,54,60,64,70,72,78,82
|
|||||
|
2
|
16
|
74
|
824871967574850703732313
|
0
|
Jarek
|
|
0,6,8,14,18,24,26,36,38,48,50,56,60,66,68,74
|
|||||
|
2
|
16
|
74
|
996689250471604163
|
0
|
Natalia Makarova
|
|
0, 6, 8, 14, 18, 24, 26, 36, 38, 48, 50, 56, 60, 66, 68, 74
|
|||||
|
3
|
16
|
94
|
320572022166380833
|
188
|
Jarek
|
|
0, 6, 10, 16, 18, 24, 28, 34, 60, 66, 70, 76, 78, 84, 88, 94
0, 88, 16, 84, 76, 24, 60, 28, 78, 10, 94, 6, 34, 66, 18, 70 |
|||||
|
3
|
16
|
94
|
320572022166380833
|
188
|
Natalia Makarova
|
|
0, 6, 10, 16, 18, 24, 28, 34, 60, 66, 70, 76, 78, 84, 88, 94
0, 88, 16, 84,76, 24, 60, 28, 78, 10, 94, 6, 34, 66, 18, 70 |
|||||
|
3
|
16
|
94
|
3848563151802671563
|
188
|
Jarek
|
|
0, 6, 10, 16, 18, 24, 28, 34, 60, 66, 70, 76, 78, 84, 88, 94
0,88,16,84,76,24,60,28,78,10,94,6,34,66,18,70 |
|||||
|
3
|
16
|
104
|
1798875821147433863
|
208
|
Jarek
|
|
0,6,14,20,24,30,38,44,60,66,74,80,84,90,98,104
0,98,20,90,80,30,60,38,84,14,104,6,44,66,24,74 |
|||||
|
3
|
16
|
122
|
1960984050584219159
|
244
|
Jarek
|
|
0,2,30,32,42,44,48,50,72,74,78,80,90,92,120,122
0,92,32,120,80,72,48,44,90,2,122,30,74,78,42,50 |
|||||
|
3
|
16
|
122
|
3919782822690082529
|
244
|
Jarek
|
|
0,12,20,32,42,48,54,60,62,68,74,80,90,102,110,122
0,110,32,102,80,54,48,62,90,20,122,12,74,60,42,68 |
|||||
|
3
|
16
|
134
|
2257802843933625383
|
268
|
Jarek
|
|
0,14,30,36,44,50,54,66,68,80,84,90,98,104,120,134
0,104,44,120,98,66,54,50,90,14,134,30,80,84,36,68 |
|||||
|
3
|
16
|
134
|
2618338000143236213
|
268
|
Jarek
|
|
0,6,8,14,30,36,38,44,90,96,98,104,120,126,128,134
0,128,14,126,104,36,90,38,120,8,134,6,44,96,30,98 |
|||||
|
3
|
16
|
136
|
3761006076207114997
|
272
|
Jarek
|
|
0,10,12,22,30,40,42,52,84,94,96,106,114,124,126,136
0,124,22,126,106,42,84,40,114,10,136,12,52,96,30,94 |
|||||
|
3
|
16
|
136
|
4363602266560571527
|
272
|
Jarek
|
|
0,10,12,22,42,52,54,64,72,82,84,94,114,124,126,136
0,124,22,126,94,54,72,52,114,10,136,12,64,84,42,82 |
|||||
|
3
|
16
|
136
|
6244416299036828467
|
272
|
Jarek
|
|
0,10,24,34,36,46,60,66,70,76,90,100,102,112,126,136
0,112,34,126,100,60,66,46,102,10,136,24,70,90,36,76 |
|||||
|
3
|
16
|
140
|
6691809871504172069
|
280
|
Jarek
|
|
0,20,30,42,48,50,62,68,72,78,90,92,98,110,120,140
0,110,50,120,98,72,48,62,90,20,140,30,92,78,42,68 |
|||||
|
3
|
16
|
146
|
196410946169488007
|
292
|
Jarek
|
|
0,20,24,42,44,60,62,66,80,84,86,102,104,122,126,146
0,122,44,126,104,66,60,62,102,20,146,24,86,84,42,80 |
|||||
|
3
|
16
|
146
|
2385895716615665027
|
292
|
Jarek
|
|
0,12,30,42,44,56,60,72,74,86,90,102,104,116,134,146
0,134,56,102,116,42,60,74,90,44,146,12,86,72,30,104 |
|||||
|
3
|
16
|
146
|
4018288550284158077
|
292
|
Jarek
|
|
0,2,12,14,42,44,54,56,90,92,102,104,132,134,144,146
0,134,14,144,104,54,90,44,132,2,146,12,56,102,42,92 |
|||||
|
3
|
16
|
146
|
5852971406868161687
|
292
|
Jarek
|
|
0,14,30,42,44,56,60,72,74,86,90,102,104,116,132,146
0,116,44,132,104,72,60,56,102,14,146,30,86,90,42,74 |
|||||
|
3
|
16
|
148
|
790313279999714941
|
296
|
Jarek
|
|
0,10,18,28,42,52,60,70,78,88,96,106,120,130,138,148
0,130,28,138,106,60,78,52,120,10,148,18,70,96,42,88 |
|||||
|
3
|
16
|
152
|
6118066623221589779
|
304
|
Jarek
|
|
0,2,30,32,42,44,72,74,78,80,108,110,120,122,150,152
0,122,32,150,110,72,78,44,120,2,152,30,74,108,42,80 |
|||||
|
3
|
16
|
154
|
3126035304223644013
|
308
|
Jarek
|
|
0,6,18,24,60,66,70,76,78,84,88,94,130,136,148,154
0,148,76,84,136,24,60,88,78,70,154,6,94,66,18,130 |
|||||
|
3
|
16
|
154
|
5908915623504697003
|
308
|
Jarek
|
|
0,6,30,36,48,54,70,76,78,84,100,106,118,124,148,154
0,148,76,84,124,36,48,100,78,70,154,6,106,54,30,118 |
|||||
|
3
|
16
|
158
|
256102275341453231
|
316
|
Jarek
|
|
0,18,20,38,42,60,62,78,80,96,98,116,120,138,140,158
0,140,38,138,116,60,78,62,120,20,158,18,80,96,42,98 |
|||||
|
3
|
16
|
158
|
2714164755369606551
|
316
|
Jarek
|
|
0,6,12,18,50,56,62,68,90,96,102,108,140,146,152,158
0,152,56,108,146,18,90,62,102,50,158,6,68,96,12,140 |
|||||
|
3
|
16
|
160
|
5848893302197701529
|
320
|
Jarek
|
|
0,12,30,42,48,60,70,78,82,90,100,112,118,130,148,160
0,148,82,90,130,42,48,100,78,70,160,12,112,60,30,118 |
|||||
|
3
|
16
|
160
|
64747964125739269
|
320
|
Jarek
|
|
0,12,30,42,58,60,70,72,88,90,100,102,118,130,148,160
0,148,70,102,130,42,60,88,90,58,160,12,100,72,30,118 |
|||||
|
3
|
16
|
164
|
1464641505981883193
|
328
|
Jarek
|
|
0,6,20,26,48,54,68,74,90,96,110,116,138,144,158,164
0,158,26,144,116,54,90,68,138,20,164,6,74,96,48,110 |
|||||
|
3
|
16
|
164
|
1960292815770022553
|
328
|
Jarek
|
|
0,14,30,36,44,50,66,80,84,98,114,120,128,134,150,164
0,134,44,150,128,66,84,50,120,14,164,30,80,114,36,98 |
|||||
|
3
|
16
|
164
|
274205528562749933
|
328
|
Jarek
|
|
0,6,30,36,44,50,74,80,84,90,114,120,128,134,158,164
0,158,50,120,134,36,84,74,114,44,164,6,80,90,30,128 |
|||||
|
3
|
16
|
164
|
2997980939880952853
|
328
|
Jarek
|
|
0,18,20,38,60,66,78,80,84,86,98,104,126,144,146,164
0,146,38,144,104,78,66,80,126,20,164,18,98,84,60,86 |
|||||
|
3
|
16
|
164
|
371373613280965583
|
328
|
Jarek
|
|
0,14,30,44,54,66,68,80,84,96,98,110,120,134,150,164
0,134,44,150,110,84,66,68,120,14,164,30,98,96,54,80 |
|||||
|
3
|
16
|
164
|
5526360461238138947
|
328
|
Jarek
|
|
0,12,20,32,42,54,62,74,90,102,110,122,132,144,152,164
0,152,32,144,122,54,90,62,132,20,164,12,74,102,42,110 |
|||||
|
3
|
16
|
164
|
6326577705299871353
|
328
|
Jarek
|
|
0,6,20,26,48,54,68,74,90,96,110,116,138,144,158,164
0,158,26,144,116,54,90,68,138,20,164,6,74,96,48,110 |
|||||
|
3
|
16
|
166
|
3616410488635421107
|
332
|
Jarek
|
|
0,10,12,22,42,52,54,64,102,112,114,124,144,154,156,166
0,154,22,156,124,54,102,52,144,10,166,12,64,114,42,112 |
|||||
|
3
|
16
|
166
|
6917484059804434777
|
332
|
Jarek
|
|
0,12,30,40,42,52,70,82,84,96,114,124,126,136,154,166
0,154,52,126,136,42,84,70,114,40,166,12,82,96,30,124 |
|||||
|
3
|
16
|
170
|
1038966937575833507
|
340
|
Jarek
|
|
0,14,30,36,44,50,66,80,90,104,120,126,134,140,156,170
0,140,44,156,134,66,90,50,126,14,170,30,80,120,36,104 |
|||||
|
3
|
16
|
170
|
1963958718695104277
|
340
|
Jarek
|
|
0,6,20,26,60,66,80,84,86,90,104,110,144,150,164,170
0,164,26,150,110,66,84,80,144,20,170,6,86,90,60,104 |
|||||
|
3
|
16
|
170
|
2845164447410820947
|
340
|
Jarek
|
|
0,20,24,44,60,66,80,84,86,90,104,110,126,146,150,170
0,146,44,150,110,84,66,80,126,20,170,24,104,90,60,86 |
|||||
|
3
|
16
|
172
|
2005475517332717239
|
344
|
Jarek
|
|
0,10,18,24,28,34,42,52,120,130,138,144,148,154,162,172
0,154,28,162,148,42,120,34,144,10,172,18,52,138,24,130 |
|||||
|
3
|
16
|
172
|
2416906123161566167
|
344
|
Jarek
|
|
0,10,36,46,60,66,70,76,96,102,106,112,126,136,162,172
0,136,46,162,112,96,66,70,126,10,172,36,106,102,60,76 |
|||||
|
3
|
16
|
172
|
3320148889158253969
|
344
|
Jarek
|
|
0,12,22,34,48,60,70,82,90,102,112,124,138,150,160,172
0,160,34,150,124,60,90,70,138,22,172,12,82,102,48,112 |
|||||
|
3
|
16
|
172
|
6943668427522772461
|
344
|
Jarek
|
|
0,10,36,46,60,66,70,76,96,102,106,112,126,136,162,172
0,136,46,162,112,96,66,70,126,10,172,36,106,102,60,76 |
|||||
|
3
|
16
|
172
|
822148161893494519
|
344
|
Jarek
|
|
0,12,28,30,40,42,58,70,102,114,130,132,142,144,160,172
0,160,40,144,142,42,102,58,132,28,172,12,70,114,30,130 |
|||||
|
3
|
16
|
176
|
1759943151645258947
|
352
|
Jarek
|
|
0,2,12,14,42,44,54,56,120,122,132,134,162,164,174,176
0,164,14,174,134,54,120,44,162,2,176,12,56,132,42,122 |
|||||
|
3
|
16
|
176
|
244890665002815107
|
352
|
Jarek
|
|
0,6,24,30,66,72,80,86,90,96,104,110,146,152,170,176
0,170,86,96,152,30,66,104,90,80,176,6,110,72,24,146 |
|||||
|
3
|
16
|
176
|
256734097976480057
|
352
|
Jarek
|
|
0,6,20,26,66,72,84,86,90,92,104,110,150,156,170,176
0,170,26,156,110,72,84,86,150,20,176,6,92,90,66,104 |
|||||
|
3
|
16
|
176
|
3954044488109204897
|
352
|
Jarek
|
|
0,6,14,20,30,36,44,50,126,132,140,146,156,162,170,176
0,170,20,162,146,36,126,44,156,14,176,6,50,132,30,140 |
|||||
|
3
|
16
|
176
|
5030319683017841117
|
352
|
Jarek
|
|
0,6,14,20,66,72,80,86,90,96,104,110,156,162,170,176
0,170,20,162,110,72,90,80,156,14,176,6,86,96,66,104 |
|||||
|
3
|
16
|
176
|
6926619233106731357
|
352
|
Jarek
|
|
0,6,20,26,66,72,84,86,90,92,104,110,150,156,170,176
0,170,26,156,110,72,84,86,150,20,176,6,92,90,66,104 |
|||||
|
3
|
16
|
178
|
125857555941397681
|
356
|
Jarek
|
|
0,10,42,48,52,58,78,88,90,100,120,126,130,136,168,178
0,136,52,168,130,90,78,58,126,10,178,42,100,120,48,88 |
|||||
|
3
|
16
|
178
|
1638289267064976151
|
356
|
Jarek
|
|
0,10,30,40,42,52,72,82,96,106,126,136,138,148,168,178
0,148,40,168,136,72,96,52,138,10,178,30,82,126,42,106 |
|||||
|
3
|
16
|
178
|
247107577536578131
|
356
|
Jarek
|
|
0,6,10,16,42,48,52,58,120,126,130,136,162,168,172,178
0,172,16,168,136,48,120,52,162,10,178,6,58,126,42,130 |
|||||
|
3
|
16
|
178
|
3580535146422008413
|
356
|
Jarek
|
|
0,4,30,34,60,64,84,88,90,94,114,118,144,148,174,178
0,148,34,174,118,90,84,64,144,4,178,30,94,114,60,88 |
|||||
|
3
|
16
|
178
|
4527086954095994641
|
356
|
Jarek
|
|
0,12,30,40,42,52,70,82,96,108,126,136,138,148,166,178
0,166,52,138,148,42,96,70,126,40,178,12,82,108,30,136 |
|||||
|
3
|
16
|
182
|
3300518070945984359
|
364
|
Jarek
|
|
0,18,20,38,60,78,80,84,98,102,104,122,144,162,164,182
0,164,38,162,122,78,84,80,144,20,182,18,98,102,60,104 |
|||||
|
3
|
16
|
182
|
6234691012623925289
|
364
|
Jarek
|
|
0,8,12,20,42,50,54,62,120,128,132,140,162,170,174,182
0,170,20,174,140,54,120,50,162,8,182,12,62,132,42,128 |
|||||
|
3
|
16
|
184
|
2104650358729544023
|
368
|
Jarek
|
|
0,6,34,40,60,66,84,90,94,100,118,124,144,150,178,184
0,178,40,150,124,66,84,94,144,34,184,6,100,90,60,118 |
|||||
|
3
|
16
|
184
|
2962098063724222219
|
368
|
Jarek
|
|
0,12,30,40,42,52,70,82,102,114,132,142,144,154,172,184
0,172,52,144,154,42,102,70,132,40,184,12,82,114,30,142 |
|||||
|
3
|
16
|
188
|
1709642327471063801
|
376
|
Jarek
|
|
0,2,30,32,60,62,90,92,96,98,126,128,156,158,186,188
0,158,32,186,128,90,96,62,156,2,188,30,92,126,60,98 |
|||||
|
3
|
16
|
188
|
3464369515329419603
|
376
|
Jarek
|
|
0,14,30,44,60,74,84,90,98,104,114,128,144,158,174,188
0,158,44,174,128,90,84,74,144,14,188,30,104,114,60,98 |
|||||
|
3
|
16
|
188
|
4308119447085349781
|
376
|
Jarek
|
|
0,6,30,36,42,48,72,78,110,116,140,146,152,158,182,188
0,182,116,78,158,36,42,140,72,110,188,6,146,48,30,152 |
|||||
|
3
|
16
|
188
|
4789518210750386921
|
376
|
Jarek
|
|
0,20,36,42,56,62,78,90,98,110,126,132,146,152,168,188
0,152,56,168,146,78,90,62,132,20,188,36,98,126,42,110 |
|||||
|
3
|
16
|
190
|
136574805190153411
|
380
|
Jarek
|
|
0,28,30,42,58,70,72,90,100,118,120,132,148,160,162,190
0,160,58,162,148,72,90,70,132,28,190,30,100,120,42,118 |
|||||
|
3
|
16
|
190
|
2970792733217448709
|
380
|
Jarek
|
|
0,10,30,40,42,52,72,82,108,118,138,148,150,160,180,190
0,160,40,180,148,72,108,52,150,10,190,30,82,138,42,118 |
|||||
|
3
|
16
|
190
|
3259520866813541389
|
380
|
Jarek
|
|
0,22,30,48,52,70,78,90,100,112,120,138,142,160,168,190
0,160,52,168,142,78,90,70,138,22,190,30,100,120,48,112 |
|||||
|
3
|
16
|
190
|
5378927763817198771
|
380
|
Jarek
|
|
0,10,42,52,60,70,78,88,102,112,120,130,138,148,180,190
0,148,52,180,130,102,78,70,138,10,190,42,112,120,60,88 |
|||||
|
3
|
16
|
190
|
543046371789268681
|
380
|
Jarek
|
|
0,10,42,52,60,70,78,88,102,112,120,130,138,148,180,190
0,148,52,180,130,102,78,70,138,10,190,42,112,120,60,88 |
|||||
|
3
|
16
|
190
|
6396263061532754749
|
380
|
Jarek
|
|
0,10,30,40,42,52,72,82,108,118,138,148,150,160,180,190
0,160,40,180,148,72,108,52,150,10,190,30,82,138,42,118 |
|||||
|
3
|
16
|
194
|
30870839193095093
|
388
|
Jarek
|
|
0,14,30,44,66,80,84,96,98,110,114,128,150,164,180,194
0,164,44,180,128,96,84,80,150,14,194,30,110,114,66,98 |
|||||
|
3
|
16
|
194
|
4051849896719838407
|
388
|
Jarek
|
|
0,12,20,32,42,54,62,74,120,132,140,152,162,174,182,194
0,182,32,174,152,54,120,62,162,20,194,12,74,132,42,140 |
|||||
|
3
|
16
|
194
|
52820951046679703
|
388
|
Jarek
|
|
0,20,24,44,66,84,86,90,104,108,110,128,150,170,174,194
0,170,44,174,128,90,84,86,150,20,194,24,110,108,66,104 |
|||||
|
3
|
16
|
194
|
7300094584443422507
|
388
|
Jarek
|
|
0,12,20,32,42,54,62,74,120,132,140,152,162,174,182,194
0,182,32,174,152,54,120,62,162,20,194,12,74,132,42,140 |
|||||
|
3
|
16
|
196
|
197328576729627247
|
392
|
Jarek
|
|
0,4,42,46,60,64,90,94,102,106,132,136,150,154,192,196
0,154,46,192,136,102,90,64,150,4,196,42,106,132,60,94 |
|||||
|
3
|
16
|
196
|
2120809189473200557
|
392
|
Jarek
|
|
0,24,36,60,66,70,90,94,102,106,126,130,136,160,172,196
0,172,94,126,160,60,66,106,102,70,196,24,130,90,36,136 |
|||||
|
3
|
16
|
196
|
2609488448804959987
|
392
|
Jarek
|
|
0,12,30,40,42,52,70,82,114,126,144,154,156,166,184,196
0,184,52,156,166,42,114,70,144,40,196,12,82,126,30,154 |
|||||
|
3
|
16
|
196
|
4418808046547962567
|
392
|
Jarek
|
|
0,12,22,34,42,54,64,76,120,132,142,154,162,174,184,196
0,184,34,174,154,54,120,64,162,22,196,12,76,132,42,142 |
|||||
|
3
|
16
|
196
|
700770556458849277
|
392
|
Jarek
|
|
0,10,24,34,42,52,66,76,120,130,144,154,162,172,186,196
0,172,34,186,154,66,120,52,162,10,196,24,76,144,42,130 |
|||||
|
3
|
16
|
200
|
4930532549661487103
|
400
|
Jarek
|
|
0,14,30,44,60,74,90,96,104,110,126,140,156,170,186,200
0,170,44,186,140,90,96,74,156,14,200,30,104,126,60,110 |
|||||
|
3
|
16
|
200
|
4960536274955735003
|
400
|
Jarek
|
|
0,14,36,50,60,74,90,96,104,110,126,140,150,164,186,200
0,164,50,186,140,96,90,74,150,14,200,36,110,126,60,104 |
|||||
|
3
|
16
|
202
|
1161886340216531929
|
404
|
Jarek
|
|
0,18,42,52,60,70,90,94,108,112,132,142,150,160,184,202
0,184,70,150,160,60,90,94,132,52,202,18,112,108,42,142 |
|||||
|
3
|
16
|
202
|
1260702715810312429
|
404
|
Jarek
|
|
0,28,30,42,58,70,72,100,102,130,132,144,160,172,174,202
0,172,58,174,160,72,102,70,144,28,202,30,100,132,42,130 |
|||||
|
3
|
16
|
202
|
3526298299878274429
|
404
|
Jarek
|
|
0,12,42,54,70,78,82,90,112,120,124,132,148,160,190,202
0,190,82,132,160,54,78,112,120,70,202,12,124,90,42,148 |
|||||
|
3
|
16
|
206
|
1184206362130402157
|
412
|
Jarek
|
|
0,30,54,56,66,84,86,96,110,120,122,140,150,152,176,206
0,176,86,150,152,84,66,110,120,56,206,30,140,96,54,122 |
|||||
|
3
|
16
|
206
|
1274498753259676961
|
412
|
Jarek
|
|
0,18,20,38,60,78,80,98,108,126,128,146,168,186,188,206
0,188,38,186,146,78,108,80,168,20,206,18,98,126,60,128 |
|||||
|
3
|
16
|
206
|
1349849386699416773
|
412
|
Jarek
|
|
0,18,48,60,66,78,80,98,108,126,128,140,146,158,188,206
0,188,98,126,158,66,60,128,108,80,206,18,146,78,48,140 |
|||||
|
3
|
16
|
206
|
1944662984243678687
|
412
|
Jarek
|
|
0,32,42,60,72,74,92,102,104,114,132,134,146,164,174,206
0,164,74,174,146,102,72,92,132,32,206,42,134,114,60,104 |
|||||
|
3
|
16
|
206
|
2454945853671281441
|
412
|
Jarek
|
|
0,18,20,38,60,78,80,98,108,126,128,146,168,186,188,206
0,188,38,186,146,78,108,80,168,20,206,18,98,126,60,128 |
|||||
|
3
|
16
|
206
|
4593033835811242937
|
412
|
Jarek
|
|
0,26,30,56,66,84,92,96,110,114,122,140,150,176,180,206
0,176,56,180,140,96,84,92,150,26,206,30,122,114,66,110 |
|||||
|
3
|
16
|
206
|
5512467165717387017
|
412
|
Jarek
|
|
0,2,30,32,42,44,72,74,132,134,162,164,174,176,204,206
0,176,32,204,164,72,132,44,174,2,206,30,74,162,42,134 |
|||||
|
3
|
16
|
206
|
584975972044768607
|
412
|
Jarek
|
|
0,6,50,56,66,72,84,90,116,122,134,140,150,156,200,206
0,200,56,156,140,72,84,116,150,50,206,6,122,90,66,134 |
|||||
|
3
|
16
|
206
|
6143618019866182577
|
412
|
Jarek
|
|
0,12,24,30,36,42,54,66,140,152,164,170,176,182,194,206
0,194,152,66,182,36,30,164,54,140,206,12,176,42,24,170 |
|||||
|
3
|
16
|
208
|
2657619911321552311
|
416
|
Jarek
|
|
0,10,36,46,60,70,96,102,106,112,138,148,162,172,198,208
0,172,46,198,148,96,102,70,162,10,208,36,106,138,60,112 |
|||||
|
3
|
16
|
208
|
3240195864372286321
|
416
|
Jarek
|
|
0,36,40,42,76,78,82,90,118,126,130,132,166,168,172,208
0,172,76,168,166,78,90,82,132,40,208,36,118,126,42,130 |
|||||
|
3
|
16
|
208
|
3288578117539863121
|
416
|
Jarek
|
|
0,28,30,42,58,70,72,100,108,136,138,150,166,178,180,208
0,178,58,180,166,72,108,70,150,28,208,30,100,138,42,136 |
|||||
|
3
|
16
|
208
|
4648589081277508711
|
416
|
Jarek
|
|
0,10,18,28,60,70,78,88,120,130,138,148,180,190,198,208
0,190,28,198,148,78,120,70,180,10,208,18,88,138,60,130 |
|||||
|
3
|
16
|
208
|
5143686234236121601
|
416
|
Jarek
|
|
0,18,22,40,60,78,82,100,108,126,130,148,168,186,190,208
0,190,40,186,148,78,108,82,168,22,208,18,100,126,60,130 |
|||||
|
3
|
16
|
208
|
5924013319890276241
|
416
|
Jarek
|
|
0,12,30,42,66,78,96,100,108,112,130,142,166,178,196,208
0,196,112,108,178,42,66,130,96,100,208,12,142,78,30,166 |
|||||
|
3
|
16
|
208
|
6460757831849769991
|
416
|
Jarek
|
|
0,12,48,60,70,78,82,90,118,126,130,138,148,160,196,208
0,196,82,138,160,60,78,118,126,70,208,12,130,90,48,148 |
|||||
|
3
|
16
|
208
|
7129286091391865041
|
416
|
Jarek
|
|
0,28,42,60,70,78,88,102,106,120,130,138,148,166,180,208
0,166,70,180,148,102,78,88,138,28,208,42,130,120,60,106 |
|||||
|
3
|
16
|
208
|
7302012435009585511
|
416
|
Jarek
|
|
0,12,60,66,70,72,78,82,126,130,136,138,142,148,196,208
0,196,82,138,148,72,66,130,126,70,208,12,142,78,60,136 |
|||||
|
3
|
16
|
212
|
1025519173619653079
|
424
|
Jarek
|
|
0,2,42,44,78,80,90,92,120,122,132,134,168,170,210,212
0,170,44,210,134,120,90,80,168,2,212,42,122,132,78,92 |
|||||
|
3
|
16
|
212
|
119890755200639999
|
424
|
Jarek
|
|
0,2,42,44,78,80,90,92,120,122,132,134,168,170,210,212
0,170,44,210,134,120,90,80,168,2,212,42,122,132,78,92 |
|||||
|
3
|
16
|
212
|
2998166279211456467
|
424
|
Jarek
|
|
0,6,30,36,50,56,80,86,126,132,156,162,176,182,206,212
0,206,56,162,182,36,126,80,156,50,212,6,86,132,30,176 |
|||||
|
3
|
16
|
212
|
3348119580392456939
|
424
|
Jarek
|
|
0,14,24,38,84,90,98,104,108,114,122,128,174,188,198,212
0,188,38,198,128,108,90,98,174,14,212,24,122,114,84,104 |
|||||
|
3
|
16
|
212
|
483563057397037421
|
424
|
Jarek
|
|
0,12,30,42,60,72,90,102,110,122,140,152,170,182,200,212
0,200,122,102,182,42,60,140,90,110,212,12,152,72,30,170 |
|||||
|
3
|
16
|
212
|
5768551885430844239
|
424
|
Jarek
|
|
0,14,30,44,78,90,92,104,108,120,122,134,168,182,198,212
0,182,44,198,134,108,90,92,168,14,212,30,122,120,78,104 |
|||||
|
3
|
16
|
214
|
121677799699349479
|
428
|
Jarek
|
|
0,10,24,34,60,70,84,94,120,130,144,154,180,190,204,214
0,190,34,204,154,84,120,70,180,10,214,24,94,144,60,130 |
|||||
|
3
|
16
|
214
|
6145034310642442003
|
428
|
Jarek
|
|
0,10,60,66,70,76,78,88,126,136,138,144,148,154,204,214
0,154,70,204,148,126,78,76,144,10,214,60,136,138,66,88 |
|||||
|
3
|
16
|
214
|
6473064433226665033
|
428
|
Jarek
|
|
0,18,30,48,70,88,96,100,114,118,126,144,166,184,196,214
0,196,88,144,184,48,96,100,126,70,214,18,118,114,30,166 |
|||||
|
3
|
16
|
214
|
6860133665885637793
|
428
|
Jarek
|
|
0,10,18,28,66,76,84,94,120,130,138,148,186,196,204,214
0,196,28,204,148,84,120,76,186,10,214,18,94,138,66,130 |
|||||
|
3
|
16
|
214
|
826028861488453243
|
428
|
Jarek
|
|
0,36,48,60,70,84,96,106,108,118,130,144,154,166,178,214
0,178,106,144,166,84,60,118,108,70,214,36,154,96,48,130 |
|||||
|
3
|
16
|
218
|
1792052806371623099
|
436
|
Jarek
|
|
0,20,30,50,78,90,98,108,110,120,128,140,168,188,198,218
0,188,50,198,140,108,90,98,168,20,218,30,128,120,78,110 |
|||||
|
3
|
16
|
218
|
3699486792695636141
|
436
|
Jarek
|
|
0,6,30,36,50,56,80,86,132,138,162,168,182,188,212,218
0,212,56,168,188,36,132,80,162,50,218,6,86,138,30,182 |
|||||
|
3
|
16
|
218
|
6837944486582519201
|
436
|
Jarek
|
|
0,12,30,36,42,48,66,78,140,152,170,176,182,188,206,218
0,206,152,78,188,42,36,170,66,140,218,12,182,48,30,176 |
|||||
|
3
|
16
|
218
|
6837953580968433689
|
436
|
Jarek
|
|
0,20,30,50,78,90,98,108,110,120,128,140,168,188,198,218
0,188,50,198,140,108,90,98,168,20,218,30,128,120,78,110 |
|||||
|
3
|
16
|
218
|
6903481620265522931
|
436
|
Jarek
|
|
0,6,30,36,56,62,86,92,126,132,156,162,182,188,212,218
0,212,62,162,188,36,126,86,156,56,218,6,92,132,30,182 |
|||||
|
3
|
16
|
220
|
1104766616538404359
|
440
|
Jarek
|
|
0,30,40,42,70,72,82,108,112,138,148,150,178,180,190,220
0,190,70,180,178,72,108,82,150,40,220,30,112,138,42,148 |
|||||
|
3
|
16
|
220
|
1977443805899164879
|
440
|
Jarek
|
|
0,30,40,42,70,72,82,108,112,138,148,150,178,180,190,220
0,190,70,180,178,72,108,82,150,40,220,30,112,138,42,148 |
|||||
|
3
|
16
|
220
|
3516575775430342843
|
440
|
Jarek
|
|
0,30,40,66,70,84,96,106,114,124,136,150,154,180,190,220
0,190,70,180,154,96,84,106,150,40,220,30,136,114,66,124 |
|||||
|
3
|
16
|
220
|
6144860086481473681
|
440
|
Jarek
|
|
0,10,42,48,52,58,90,100,120,130,162,168,172,178,210,220
0,178,52,210,172,90,120,58,168,10,220,42,100,162,48,130 |
|||||
|
3
|
16
|
224
|
1353204408659434493
|
448
|
Jarek
|
|
0,24,30,54,84,86,108,110,114,116,138,140,170,194,200,224
0,200,110,138,194,54,84,116,114,86,224,24,140,108,30,170 |
|||||
|
3
|
16
|
224
|
1365986292501549617
|
448
|
Jarek
|
|
0,30,42,62,72,90,92,104,120,132,134,152,162,182,194,224
0,194,92,162,182,72,90,104,132,62,224,30,134,120,42,152 |
|||||
|
3
|
16
|
224
|
1836717961457293283
|
448
|
Jarek
|
|
0,24,50,66,74,84,90,108,116,134,140,150,158,174,200,224
0,200,74,174,158,90,84,116,150,50,224,24,140,108,66,134 |
|||||
|
3
|
16
|
224
|
3211471911994853333
|
448
|
Jarek
|
|
0,26,30,54,56,80,84,110,114,140,144,168,170,194,198,224
0,194,56,198,170,84,114,80,168,26,224,30,110,144,54,140 |
|||||
|
3
|
16
|
224
|
3535827318958835063
|
448
|
Jarek
|
|
0,18,20,38,60,78,80,98,126,144,146,164,186,204,206,224
0,206,38,204,164,78,126,80,186,20,224,18,98,144,60,146 |
|||||
|
3
|
16
|
224
|
3676207202733217613
|
448
|
Jarek
|
|
0,24,30,54,84,86,108,110,114,116,138,140,170,194,200,224
0,200,110,138,194,54,84,116,114,86,224,24,140,108,30,170 |
|||||
|
3
|
16
|
224
|
3925937432649879263
|
448
|
Jarek
|
|
0,14,30,44,66,80,96,110,114,128,144,158,180,194,210,224
0,194,44,210,158,96,114,80,180,14,224,30,110,144,66,128 |
|||||
|
3
|
16
|
224
|
4072432651991186423
|
448
|
Jarek
|
|
0,6,14,20,30,36,44,50,174,180,188,194,204,210,218,224
0,218,20,210,194,36,174,44,204,14,224,6,50,180,30,188 |
|||||
|
3
|
16
|
224
|
858132626286456923
|
448
|
Jarek
|
|
0,6,50,56,78,84,90,96,128,134,140,146,168,174,218,224
0,218,56,174,146,84,90,128,168,50,224,6,134,96,78,140 |
|||||
|
3
|
16
|
226
|
1348850943815472523
|
452
|
Jarek
|
|
0,30,40,60,70,90,96,100,126,130,136,156,166,186,196,226
0,196,70,186,166,90,96,100,156,40,226,30,130,126,60,136 |
|||||
|
3
|
16
|
226
|
2743915961319802891
|
452
|
Jarek
|
|
0,18,30,40,48,58,70,88,138,156,168,178,186,196,208,226
0,208,58,186,196,48,138,70,168,40,226,18,88,156,30,178 |
|||||
|
3
|
16
|
226
|
4386788379691729507
|
452
|
Jarek
|
|
0,12,30,42,70,82,100,112,114,126,144,156,184,196,214,226
0,214,82,156,196,42,114,100,144,70,226,12,112,126,30,184 |
|||||
|
3
|
16
|
226
|
5419298383390453957
|
452
|
Jarek
|
|
0,30,42,64,72,90,94,106,120,132,136,154,162,184,196,226
0,196,94,162,184,72,90,106,132,64,226,30,136,120,42,154 |
|||||
|
3
|
16
|
226
|
5428670927917516177
|
452
|
Jarek
|
|
0,6,16,22,84,90,100,106,120,126,136,142,204,210,220,226
0,220,22,210,142,90,120,100,204,16,226,6,106,126,84,136 |
|||||
|
3
|
16
|
226
|
6205884072061035403
|
452
|
Jarek
|
|
0,18,48,66,70,88,90,108,118,136,138,156,160,178,208,226
0,208,88,156,178,66,90,118,138,70,226,18,136,108,48,160 |
|||||
|
3
|
16
|
226
|
75219020808006217
|
452
|
Jarek
|
|
0,6,36,42,70,76,106,112,114,120,150,156,184,190,220,226
0,220,76,156,190,42,114,106,150,70,226,6,112,120,36,184 |
|||||
|
3
|
16
|
226
|
983481025217213137
|
452
|
Jarek
|
|
0,30,40,70,72,84,102,112,114,124,142,154,156,186,196,226
0,196,70,186,154,102,84,112,156,40,226,30,142,114,72,124 |
|||||
|
3
|
16
|
230
|
1013817764091131963
|
460
|
Jarek
|
|
0,20,36,56,84,90,104,110,120,126,140,146,174,194,210,230
0,194,56,210,146,120,90,104,174,20,230,36,140,126,84,110 |
|||||
|
3
|
16
|
230
|
1161621187363787303
|
460
|
Jarek
|
|
0,14,30,44,60,74,90,104,126,140,156,170,186,200,216,230
0,200,44,216,170,90,126,74,186,14,230,30,104,156,60,140 |
|||||
|
3
|
16
|
230
|
2746765265140004819
|
460
|
Jarek
|
|
0,8,12,20,90,98,102,110,120,128,132,140,210,218,222,230
0,218,20,222,140,102,120,98,210,8,230,12,110,132,90,128 |
|||||
|
3
|
16
|
230
|
2849547638609642513
|
460
|
Jarek
|
|
0,26,30,56,60,86,90,114,116,140,144,170,174,200,204,230
0,200,56,204,170,90,114,86,174,26,230,30,116,144,60,140 |
|||||
|
3
|
16
|
230
|
3284360538807735461
|
460
|
Jarek
|
|
0,12,20,32,78,90,98,110,120,132,140,152,198,210,218,230
0,218,32,210,152,90,120,98,198,20,230,12,110,132,78,140 |
|||||
|
3
|
16
|
230
|
3808061696393625101
|
460
|
Jarek
|
|
0,2,30,32,60,62,90,92,138,140,168,170,198,200,228,230
0,200,32,228,170,90,138,62,198,2,230,30,92,168,60,140 |
|||||
|
3
|
16
|
230
|
5554064482809089477
|
460
|
Jarek
|
|
0,14,60,66,74,80,90,104,126,140,150,156,164,170,216,230
0,170,74,216,164,126,90,80,156,14,230,60,140,150,66,104 |
|||||
|
3
|
16
|
230
|
6044277931660903169
|
460
|
Jarek
|
|
0,20,30,48,50,68,78,98,132,152,162,180,182,200,210,230
0,200,50,210,182,78,132,68,180,20,230,30,98,162,48,152 |
|||||
|
3
|
16
|
232
|
1949587307274796249
|
464
|
Jarek
|
|
0,22,42,64,78,90,100,112,120,132,142,154,168,190,210,232
0,190,64,210,154,120,90,100,168,22,232,42,142,132,78,112 |
|||||
|
3
|
16
|
232
|
2739157114418172739
|
464
|
Jarek
|
|
0,30,48,70,78,84,100,114,118,132,148,154,162,184,202,232
0,202,100,162,184,78,84,118,132,70,232,30,148,114,48,154 |
|||||
|
3
|
16
|
232
|
4669370734348914049
|
464
|
Jarek
|
|
0,10,42,52,60,70,102,112,120,130,162,172,180,190,222,232
0,190,52,222,172,102,120,70,180,10,232,42,112,162,60,130 |
|||||
|
3
|
16
|
232
|
4769304739639109671
|
464
|
Jarek
|
|
0,36,60,66,70,96,102,106,126,130,136,162,166,172,196,232
0,196,106,162,172,96,66,130,126,70,232,36,166,102,60,136 |
|||||
|
3
|
16
|
232
|
4854227454119376679
|
464
|
Jarek
|
|
0,10,24,34,90,100,108,114,118,124,132,142,198,208,222,232
0,208,34,222,142,114,108,100,198,10,232,24,124,132,90,118 |
|||||
|
3
|
16
|
232
|
5430518283273066469
|
464
|
Jarek
|
|
0,22,30,48,52,70,78,100,132,154,162,180,184,202,210,232
0,202,52,210,184,78,132,70,180,22,232,30,100,162,48,154 |
|||||
|
3
|
16
|
232
|
6455528034823901701
|
464
|
Jarek
|
|
0,6,66,70,72,76,90,96,136,142,156,160,162,166,226,232
0,226,76,162,166,72,90,136,156,70,232,6,142,96,66,160 |
|||||
|
3
|
16
|
232
|
942188212207026139
|
464
|
Jarek
|
|
0,18,24,42,60,78,84,102,130,148,154,172,190,208,214,232
0,214,148,102,208,42,60,154,84,130,232,18,172,78,24,190 |
|||||
|
3
|
16
|
236
|
1748611243534828247
|
472
|
Jarek
|
|
0,24,26,50,60,84,86,110,126,150,152,176,186,210,212,236
0,212,50,210,176,84,126,86,186,26,236,24,110,150,60,152 |
|||||
|
3
|
16
|
236
|
4814184375353087117
|
472
|
Jarek
|
|
0,12,42,50,54,62,92,104,132,144,174,182,186,194,224,236
0,224,62,186,194,54,132,92,174,50,236,12,104,144,42,182 |
|||||
|
3
|
16
|
236
|
5172657399101044427
|
472
|
Jarek
|
|
0,42,50,60,84,92,102,110,126,134,144,152,176,186,194,236
0,194,92,186,176,102,84,110,144,50,236,42,152,126,60,134 |
|||||
|
3
|
16
|
236
|
597511709585678627
|
472
|
Jarek
|
|
0,6,20,26,36,42,56,62,174,180,194,200,210,216,230,236
0,230,26,216,200,42,174,56,210,20,236,6,62,180,36,194 |
|||||
|
3
|
16
|
238
|
1111443560879387521
|
476
|
Jarek
|
|
0,42,60,66,70,102,108,112,126,130,136,168,172,178,196,238
0,196,112,168,178,102,66,130,126,70,238,42,172,108,60,136 |
|||||
|
3
|
16
|
238
|
1684157406173732383
|
476
|
Jarek
|
|
0,4,24,28,60,64,84,88,150,154,174,178,210,214,234,238
0,214,28,234,178,84,150,64,210,4,238,24,88,174,60,154 |
|||||
|
3
|
16
|
238
|
1722099695477586181
|
476
|
Jarek
|
|
0,12,28,30,40,42,58,70,168,180,196,198,208,210,226,238
0,226,40,210,208,42,168,58,198,28,238,12,70,180,30,196 |
|||||
|
3
|
16
|
238
|
2870027314708591981
|
476
|
Jarek
|
|
0,30,42,58,72,88,100,108,130,138,150,166,180,196,208,238
0,208,88,180,196,72,108,100,150,58,238,30,130,138,42,166 |
|||||
|
3
|
16
|
238
|
3330362879526931471
|
476
|
Jarek
|
|
0,18,42,60,70,88,108,112,126,130,150,168,178,196,220,238
0,220,88,168,196,60,108,112,150,70,238,18,130,126,42,178 |
|||||
|
3
|
16
|
238
|
520330171849862431
|
476
|
Jarek
|
|
0,12,18,28,30,40,46,58,180,192,198,208,210,220,226,238
0,226,40,210,220,30,180,46,198,28,238,12,58,192,18,208 |
|||||
|
3
|
16
|
238
|
5990853535865174191
|
476
|
Jarek
|
|
0,10,42,52,78,88,108,118,120,130,150,160,186,196,228,238
0,196,52,228,160,120,108,88,186,10,238,42,130,150,78,118 |
|||||
|
3
|
16
|
238
|
6245958363138445849
|
476
|
Jarek
|
|
0,10,24,34,84,94,108,118,120,130,144,154,204,214,228,238
0,214,34,228,154,108,120,94,204,10,238,24,118,144,84,130 |
|||||
|
3
|
16
|
238
|
6828326467141699951
|
476
|
Jarek
|
|
0,12,36,48,70,82,106,118,120,132,156,168,190,202,226,238
0,226,82,168,202,48,120,106,156,70,238,12,118,132,36,190 |
|||||
|
3
|
16
|
242
|
470383969303868849
|
484
|
Jarek
|
|
0,12,48,50,60,62,98,110,132,144,180,182,192,194,230,242
0,230,62,192,194,60,132,98,180,50,242,12,110,144,48,182 |
|||||
|
3
|
16
|
242
|
505751676098073269
|
484
|
Jarek
|
|
0,12,30,42,60,72,90,102,140,152,170,182,200,212,230,242
0,230,152,102,212,42,60,170,90,140,242,12,182,72,30,200 |
|||||
|
3
|
16
|
242
|
6276472529120900609
|
484
|
Jarek
|
|
0,18,42,60,72,90,110,114,128,132,152,170,182,200,224,242
0,224,128,132,200,60,72,152,114,110,242,18,170,90,42,182 |
|||||
|
3
|
16
|
242
|
854802325142674739
|
484
|
Jarek
|
|
0,12,42,54,68,80,110,120,122,132,162,174,188,200,230,242
0,230,80,174,200,54,120,110,162,68,242,12,122,132,42,188 |
|||||
|
3
|
16
|
244
|
1422162363915832963
|
488
|
Jarek
|
|
0,36,40,48,76,84,88,120,124,156,160,168,196,204,208,244
0,208,76,204,196,84,120,88,168,40,244,36,124,156,48,160 |
|||||
|
3
|
16
|
244
|
1695576612355403647
|
488
|
Jarek
|
|
0,24,60,70,84,90,94,114,130,150,154,160,174,184,220,244
0,220,94,174,184,84,90,130,150,70,244,24,154,114,60,160 |
|||||
|
3
|
16
|
244
|
193747830997541713
|
488
|
Jarek
|
|
0,18,28,46,60,78,88,106,138,156,166,184,198,216,226,244
0,226,46,216,184,78,138,88,198,28,244,18,106,156,60,166 |
|||||
|
3
|
16
|
244
|
2877019027302762913
|
488
|
Jarek
|
|
0,6,54,60,70,76,114,120,124,130,168,174,184,190,238,244
0,238,76,174,190,60,114,124,168,70,244,6,130,120,54,184 |
|||||
|
3
|
16
|
244
|
2996774562519515923
|
488
|
Jarek
|
|
0,40,54,66,84,94,106,120,124,138,150,160,178,190,204,244
0,190,94,204,178,120,84,106,150,40,244,54,160,138,66,124 |
|||||
|
3
|
16
|
244
|
4590873012397692739
|
488
|
Jarek
|
|
0,12,42,54,70,82,112,120,124,132,162,174,190,202,232,244
0,232,82,174,202,54,120,112,162,70,244,12,124,132,42,190 |
|||||
|
3
|
16
|
244
|
5229591821941140757
|
488
|
Jarek
|
|
0,12,42,54,70,82,112,120,124,132,162,174,190,202,232,244
0,232,82,174,202,54,120,112,162,70,244,12,124,132,42,190 |
|||||
|
3
|
16
|
244
|
593606097226087453
|
488
|
Jarek
|
|
0,18,40,58,60,78,100,118,126,144,166,184,186,204,226,244
0,226,58,204,184,78,126,100,186,40,244,18,118,144,60,166 |
|||||
|
3
|
16
|
244
|
5986294670848092703
|
488
|
Jarek
|
|
0,6,40,46,84,90,114,120,124,130,154,160,198,204,238,244
0,238,46,204,160,90,114,124,198,40,244,6,130,120,84,154 |
|||||
|
3
|
16
|
244
|
6095019077256106423
|
488
|
Jarek
|
|
0,18,66,70,84,88,90,108,136,154,156,160,174,178,226,244
0,226,88,174,178,84,90,136,156,70,244,18,154,108,66,160 |
|||||
|
3
|
16
|
244
|
6218513221849930999
|
488
|
Jarek
|
|
0,30,40,60,70,90,100,114,130,144,154,174,184,204,214,244
0,214,70,204,184,90,114,100,174,40,244,30,130,144,60,154 |
|||||
|
3
|
16
|
248
|
2187508254185189591
|
496
|
Jarek
|
|
0,42,60,66,80,102,108,122,126,140,146,168,182,188,206,248
0,206,122,168,188,102,66,140,126,80,248,42,182,108,60,146 |
|||||
|
3
|
16
|
250
|
4372961435616492067
|
500
|
Jarek
|
|
0,6,24,30,70,76,94,100,150,156,174,180,220,226,244,250
0,244,76,180,226,30,150,94,174,70,250,6,100,156,24,220 |
|||||
|
3
|
16
|
250
|
6632564174879375731
|
500
|
Jarek
|
|
0,18,60,70,78,88,102,120,130,148,162,172,180,190,232,250
0,232,88,180,190,78,102,130,162,70,250,18,148,120,60,172 |
|||||
|
3
|
16
|
250
|
6895412835092216299
|
500
|
Jarek
|
|
0,12,28,40,90,102,118,120,130,132,148,160,210,222,238,250
0,238,40,222,160,102,120,118,210,28,250,12,130,132,90,148 |
|||||
|
3
|
16
|
254
|
1548843198482789639
|
508
|
Jarek
|
|
0,30,42,50,72,80,92,122,132,162,174,182,204,212,224,254
0,224,80,204,212,72,132,92,174,50,254,30,122,162,42,182 |
|||||
|
3
|
16
|
254
|
4571312291409422243
|
508
|
Jarek
|
|
0,20,24,44,60,80,84,104,150,170,174,194,210,230,234,254
0,230,44,234,194,84,150,80,210,20,254,24,104,174,60,170 |
|||||
|
3
|
16
|
256
|
183654607712944657
|
512
|
Jarek
|
|
0,24,42,60,66,84,102,126,130,154,172,190,196,214,232,256
0,232,154,126,214,66,60,172,102,130,256,24,196,84,42,190 |
|||||
|
3
|
16
|
256
|
1991122514241536437
|
512
|
Jarek
|
|
0,12,42,54,100,102,112,114,142,144,154,156,202,214,244,256
0,244,112,156,214,54,102,142,144,100,256,12,154,114,42,202 |
|||||
|
3
|
16
|
256
|
2370832941679372567
|
512
|
Jarek
|
|
0,12,22,34,90,102,112,124,132,144,154,166,222,234,244,256
0,244,34,234,166,102,132,112,222,22,256,12,124,144,90,154 |
|||||
|
3
|
16
|
256
|
2901380697433271107
|
512
|
Jarek
|
|
0,40,42,54,82,94,96,120,136,160,162,174,202,214,216,256
0,214,82,216,202,96,120,94,174,40,256,42,136,162,54,160 |
|||||
|
3
|
16
|
256
|
3754487283109755883
|
512
|
Jarek
|
|
0,18,48,66,70,88,118,120,136,138,168,186,190,208,238,256
0,238,88,186,208,66,120,118,168,70,256,18,136,138,48,190 |
|||||
|
3
|
16
|
256
|
5386876445300866597
|
512
|
Jarek
|
|
0,30,42,72,82,102,112,124,132,144,154,174,184,214,226,256
0,226,112,174,214,72,102,124,144,82,256,30,154,132,42,184 |
|||||
|
3
|
16
|
256
|
5502527692824783637
|
512
|
Jarek
|
|
0,24,46,60,70,84,106,126,130,150,172,186,196,210,232,256
0,232,70,210,196,84,126,106,186,46,256,24,130,150,60,172 |
|||||
|
3
|
16
|
256
|
724964620942114237
|
512
|
Jarek
|
|
0,12,42,54,90,102,112,124,132,144,154,166,202,214,244,256
0,244,124,144,214,54,90,154,132,112,256,12,166,102,42,202 |
|||||
|
3
|
16
|
260
|
1115116970440210853
|
520
|
Jarek
|
|
0,20,66,84,86,90,104,110,150,156,170,174,176,194,240,260
0,194,86,240,176,150,90,104,174,20,260,66,170,156,84,110 |
|||||
|
3
|
16
|
260
|
172234415276027219
|
520
|
Jarek
|
|
0,20,42,48,62,68,90,110,150,170,192,198,212,218,240,260
0,218,62,240,212,90,150,68,198,20,260,42,110,192,48,170 |
|||||
|
3
|
16
|
260
|
4136769267384711527
|
520
|
Jarek
|
|
0,26,30,56,84,110,114,120,140,146,150,176,204,230,234,260
0,230,56,234,176,114,120,110,204,26,260,30,140,150,84,146 |
|||||
|
3
|
16
|
260
|
4949096256248126783
|
520
|
Jarek
|
|
0,30,36,66,84,110,114,120,140,146,150,176,194,224,230,260
0,230,140,150,224,66,84,146,120,110,260,30,176,114,36,194 |
|||||
|
3
|
16
|
260
|
576195018029325059
|
520
|
Jarek
|
|
0,18,60,78,80,98,102,120,140,158,162,180,182,200,242,260
0,242,98,180,200,78,102,140,162,80,260,18,158,120,60,182 |
|||||
|
3
|
16
|
260
|
970723521259217267
|
520
|
Jarek
|
|
0,20,24,44,66,86,90,110,150,170,174,194,216,236,240,260
0,236,44,240,194,90,150,86,216,20,260,24,110,174,66,170 |
|||||
|
3
|
16
|
262
|
1394323695407632369
|
524
|
Jarek
|
|
0,22,30,52,78,100,108,130,132,154,162,184,210,232,240,262
0,232,52,240,184,108,132,100,210,22,262,30,130,162,78,154 |
|||||
|
3
|
16
|
262
|
523223163845273719
|
524
|
Jarek
|
|
0,18,42,60,70,88,112,130,132,150,174,192,202,220,244,262
0,244,88,192,220,60,132,112,174,70,262,18,130,150,42,202 |
|||||
|
3
|
16
|
262
|
6739882649149671649
|
524
|
Jarek
|
|
0,18,42,60,90,108,112,130,132,150,154,172,202,220,244,262
0,244,130,150,220,60,90,154,132,112,262,18,172,108,42,202 |
|||||
|
3
|
16
|
262
|
90658333138283839
|
524
|
Jarek
|
|
0,40,42,48,82,88,90,130,132,172,174,180,214,220,222,262
0,220,82,222,214,90,132,88,180,40,262,42,130,174,48,172 |
|||||
|
3
|
16
|
266
|
1662966605198077337
|
532
|
Jarek
|
|
0,14,42,56,90,104,120,132,134,146,162,176,210,224,252,266
0,224,56,252,176,132,120,104,210,14,266,42,146,162,90,134 |
|||||
|
3
|
16
|
266
|
3674413084938709037
|
532
|
Jarek
|
|
0,12,30,42,84,96,114,126,140,152,170,182,224,236,254,266
0,254,152,126,236,42,84,170,114,140,266,12,182,96,30,224 |
|||||
|
3
|
16
|
266
|
4276861062256425977
|
532
|
Jarek
|
|
0,24,36,60,66,90,102,126,140,164,176,200,206,230,242,266
0,242,164,126,230,60,66,176,102,140,266,24,200,90,36,206 |
|||||
|
3
|
16
|
266
|
5388267171062582297
|
532
|
Jarek
|
|
0,24,30,54,72,96,102,126,140,164,170,194,212,236,242,266
0,242,164,126,236,54,72,170,102,140,266,24,194,96,30,212 |
|||||
|
3
|
16
|
266
|
65659672001596307
|
532
|
Jarek
|
|
0,24,60,66,84,90,116,126,140,150,176,182,200,206,242,266
0,242,140,150,206,84,66,176,126,116,266,24,200,90,60,182 |
|||||
|
3
|
16
|
266
|
6894646511664746207
|
532
|
Jarek
|
|
0,24,36,60,66,90,102,126,140,164,176,200,206,230,242,266
0,242,164,126,230,60,66,176,102,140,266,24,200,90,36,206 |
|||||
|
3
|
16
|
268
|
331797868801711441
|
536
|
Jarek
|
|
0,22,30,52,90,112,120,126,142,148,156,178,216,238,246,268
0,238,52,246,178,120,126,112,216,22,268,30,142,156,90,148 |
|||||
|
3
|
16
|
268
|
3551657267160637651
|
536
|
Jarek
|
|
0,30,48,70,78,100,118,120,148,150,168,190,198,220,238,268
0,238,100,198,220,78,120,118,168,70,268,30,148,150,48,190 |
|||||
|
3
|
16
|
268
|
3561150466636039561
|
536
|
Jarek
|
|
0,36,42,60,78,96,102,130,138,166,172,190,208,226,232,268
0,232,166,138,226,78,60,172,102,130,268,36,208,96,42,190 |
|||||
|
3
|
16
|
268
|
392952504670299499
|
536
|
Jarek
|
|
0,30,48,70,78,100,118,120,148,150,168,190,198,220,238,268
0,238,100,198,220,78,120,118,168,70,268,30,148,150,48,190 |
|||||
|
3
|
16
|
268
|
573863571825332491
|
536
|
Jarek
|
|
0,30,42,72,76,106,118,120,148,150,162,192,196,226,238,268
0,238,106,192,226,72,120,118,162,76,268,30,148,150,42,196 |
|||||
|
3
|
16
|
268
|
7238777982941181361
|
536
|
Jarek
|
|
0,60,66,70,72,126,130,132,136,138,142,196,198,202,208,268
0,208,130,198,202,126,72,136,138,70,268,60,196,132,66,142 |
|||||
|
3
|
16
|
272
|
2055009868507385459
|
544
|
Jarek
|
|
0,42,48,50,90,92,98,132,140,174,180,182,222,224,230,272
0,230,92,222,224,90,132,98,180,50,272,42,140,174,48,182 |
|||||
|
3
|
16
|
272
|
213896077666130459
|
544
|
Jarek
|
|
0,20,42,62,90,110,120,132,140,152,162,182,210,230,252,272
0,230,62,252,182,132,120,110,210,20,272,42,152,162,90,140 |
|||||
|
3
|
16
|
272
|
3617374549635817109
|
544
|
Jarek
|
|
0,38,42,80,90,102,128,132,140,144,170,182,192,230,234,272
0,230,80,234,182,132,102,128,192,38,272,42,170,144,90,140 |
|||||
|
3
|
16
|
272
|
5051144543625838907
|
544
|
Jarek
|
|
0,6,30,36,90,96,120,126,146,152,176,182,236,242,266,272
0,266,152,126,242,36,90,176,120,146,272,6,182,96,30,236 |
|||||
|
3
|
16
|
274
|
1161374752701595303
|
548
|
Jarek
|
|
0,18,60,70,78,88,126,130,144,148,186,196,204,214,256,274
0,256,88,204,214,78,126,130,186,70,274,18,148,144,60,196 |
|||||
|
3
|
16
|
274
|
146740177075293973
|
548
|
Jarek
|
|
0,30,40,66,70,96,106,136,138,168,178,204,208,234,244,274
0,244,70,234,208,96,138,106,204,40,274,30,136,168,66,178 |
|||||
|
3
|
16
|
274
|
3069372153044336233
|
548
|
Jarek
|
|
0,34,66,84,90,100,118,124,150,156,174,184,190,208,240,274
0,208,100,240,190,150,90,118,174,34,274,66,184,156,84,124 |
|||||
|
3
|
16
|
274
|
3326474066397256183
|
548
|
Jarek
|
|
0,30,36,40,66,70,76,106,168,198,204,208,234,238,244,274
0,244,70,234,238,66,168,76,204,40,274,30,106,198,36,208 |
|||||
|
3
|
16
|
274
|
5075754267051808903
|
548
|
Jarek
|
|
0,6,30,36,84,90,114,120,154,160,184,190,238,244,268,274
0,268,160,120,244,36,84,184,114,154,274,6,190,90,30,238 |
|||||
|
3
|
16
|
274
|
7002957165963385603
|
548
|
Jarek
|
|
0,4,60,64,84,88,126,130,144,148,186,190,210,214,270,274
0,214,64,270,190,144,126,88,210,4,274,60,148,186,84,130 |
|||||
|
3
|
16
|
278
|
2202676356250302461
|
556
|
Jarek
|
|
0,6,36,42,96,102,132,138,140,146,176,182,236,242,272,278
0,272,146,138,242,42,96,176,132,140,278,6,182,102,36,236 |
|||||
|
3
|
16
|
278
|
2657370364046282393
|
556
|
Jarek
|
|
0,14,54,68,90,104,120,134,144,158,174,188,210,224,264,278
0,224,68,264,188,144,120,104,210,14,278,54,158,174,90,134 |
|||||
|
3
|
16
|
278
|
4303654267764620861
|
556
|
Jarek
|
|
0,30,36,66,72,102,108,138,140,170,176,206,212,242,248,278
0,248,170,138,242,66,72,176,108,140,278,30,206,102,36,212 |
|||||
|
3
|
16
|
278
|
4751478919613173733
|
556
|
Jarek
|
|
0,20,24,44,84,104,108,128,150,170,174,194,234,254,258,278
0,254,44,258,194,108,150,104,234,20,278,24,128,174,84,170 |
|||||
|
3
|
16
|
280
|
108978576749718703
|
560
|
Jarek
|
|
0,30,66,70,96,100,114,136,144,166,180,184,210,214,250,280
0,250,100,210,214,96,114,136,180,70,280,30,166,144,66,184 |
|||||
|
3
|
16
|
280
|
1152127746876591217
|
560
|
Jarek
|
|
0,10,36,46,84,94,120,130,150,160,186,196,234,244,270,280
0,244,46,270,196,120,150,94,234,10,280,36,130,186,84,160 |
|||||
|
3
|
16
|
280
|
2381171917182771109
|
560
|
Jarek
|
|
0,42,60,88,90,102,130,132,148,150,178,190,192,220,238,280
0,238,130,192,220,102,90,148,150,88,280,42,190,132,60,178 |
|||||
|
3
|
16
|
280
|
3000609520074222541
|
560
|
Jarek
|
|
0,18,60,78,90,108,112,130,150,168,172,190,202,220,262,280
0,262,130,168,220,78,90,172,150,112,280,18,190,108,60,202 |
|||||
|
3
|
16
|
280
|
3919037389119084523
|
560
|
Jarek
|
|
0,30,40,70,84,114,124,126,154,156,166,196,210,240,250,280
0,250,70,240,196,114,126,124,210,40,280,30,154,156,84,166 |
|||||
|
3
|
16
|
280
|
6232062498622812853
|
560
|
Jarek
|
|
0,16,30,46,84,100,114,130,150,166,180,196,234,250,264,280
0,250,46,264,196,114,150,100,234,16,280,30,130,180,84,166 |
|||||
|
3
|
16
|
280
|
632878876266807217
|
560
|
Jarek
|
|
0,4,60,64,90,94,126,130,150,154,186,190,216,220,276,280
0,220,64,276,190,150,126,94,216,4,280,60,154,186,90,130 |
|||||
|
3
|
16
|
280
|
7288094093539270027
|
560
|
Jarek
|
|
0,46,60,84,90,106,130,136,144,150,174,190,196,220,234,280
0,220,106,234,196,144,90,130,174,46,280,60,190,150,84,136 |
|||||
|
3
|
16
|
280
|
87883992459664963
|
560
|
Jarek
|
|
0,46,60,84,90,106,130,136,144,150,174,190,196,220,234,280
0,220,106,234,196,144,90,130,174,46,280,60,190,150,84,136 |
|||||
|
3
|
16
|
282
|
1023267524341869299
|
564
|
Jarek
|
|
0,30,48,78,84,114,120,132,150,162,168,198,204,234,252,282
0,234,78,252,198,132,120,114,204,30,282,48,162,168,84,150 |
|||||
|
3
|
16
|
282
|
4367495951483424229
|
564
|
Jarek
|
|
0,12,18,30,42,54,60,72,210,222,228,240,252,264,270,282
0,264,30,270,240,60,210,54,252,12,282,18,72,228,42,222 |
|||||
|
3
|
16
|
284
|
135636084688856267
|
568
|
Jarek
|
|
0,42,50,60,92,102,110,132,152,174,182,192,224,234,242,284
0,242,92,234,224,102,132,110,192,50,284,42,152,174,60,182 |
|||||
|
3
|
16
|
284
|
2435735862630081383
|
568
|
Jarek
|
|
0,30,36,50,66,80,86,116,168,198,204,218,234,248,254,284
0,254,80,234,248,66,168,86,204,50,284,30,116,198,36,218 |
|||||
|
3
|
16
|
284
|
2466954089329721129
|
568
|
Jarek
|
|
0,12,42,54,90,102,132,140,144,152,182,194,230,242,272,284
0,272,152,144,242,54,90,182,132,140,284,12,194,102,42,230 |
|||||
|
3
|
16
|
284
|
3684541435048485383
|
568
|
Jarek
|
|
0,30,36,50,66,80,86,116,168,198,204,218,234,248,254,284
0,254,80,234,248,66,168,86,204,50,284,30,116,198,36,218 |
|||||
|
3
|
16
|
284
|
4276130160796247363
|
568
|
Jarek
|
|
0,30,56,78,86,108,120,134,150,164,176,198,206,228,254,284
0,254,86,228,206,108,120,134,198,56,284,30,164,150,78,176 |
|||||
|
3
|
16
|
284
|
501455933430730433
|
568
|
Jarek
|
|
0,18,56,60,74,78,116,134,150,168,206,210,224,228,266,284
0,266,74,228,224,78,150,116,210,56,284,18,134,168,60,206 |
|||||
|
3
|
16
|
284
|
5309126148402591029
|
568
|
Jarek
|
|
0,12,42,54,60,72,102,114,170,182,212,224,230,242,272,284
0,272,182,114,242,54,60,212,102,170,284,12,224,72,42,230 |
|||||
|
3
|
16
|
286
|
2529635432547452107
|
572
|
Jarek
|
|
0,40,42,82,90,114,130,132,154,156,172,196,204,244,246,286
0,244,82,246,196,132,114,130,204,40,286,42,172,156,90,154 |
|||||
|
3
|
16
|
286
|
2959720113369490771
|
572
|
Jarek
|
|
0,28,48,60,76,88,108,136,150,178,198,210,226,238,258,286
0,238,76,258,226,108,150,88,210,28,286,48,136,198,60,178 |
|||||
|
3
|
16
|
286
|
369819834773439997
|
572
|
Jarek
|
|
0,46,66,84,90,112,130,136,150,156,174,196,202,220,240,286
0,220,112,240,202,150,90,130,174,46,286,66,196,156,84,136 |
|||||
|
3
|
16
|
286
|
3901689256438869307
|
572
|
Jarek
|
|
0,24,46,66,70,90,112,136,150,174,196,216,220,240,262,286
0,262,70,240,220,90,150,112,216,46,286,24,136,174,66,196 |
|||||
|
3
|
16
|
286
|
605112013859711227
|
572
|
Jarek
|
|
0,30,42,72,84,114,126,130,156,160,172,202,214,244,256,286
0,256,160,156,244,72,84,172,126,130,286,30,202,114,42,214 |
|||||
|
3
|
16
|
286
|
64357903328718397
|
572
|
Jarek
|
|
0,6,10,16,126,132,136,142,144,150,154,160,270,276,280,286
0,280,16,276,160,132,144,136,270,10,286,6,142,150,126,154 |
|||||
|
3
|
16
|
286
|
973289520281889157
|
572
|
Jarek
|
|
0,42,54,70,96,112,120,124,162,166,174,190,216,232,244,286
0,244,112,216,232,96,120,124,174,70,286,42,166,162,54,190 |
|||||
|
3
|
16
|
290
|
2779503923057699879
|
580
|
Jarek
|
|
0,18,42,60,90,108,132,140,150,158,182,200,230,248,272,290
0,272,158,150,248,60,90,182,132,140,290,18,200,108,42,230 |
|||||
|
3
|
16
|
290
|
4293822215103776063
|
580
|
Jarek
|
|
0,30,36,66,90,120,126,134,156,164,170,200,224,254,260,290
0,260,164,156,254,66,90,170,126,134,290,30,200,120,36,224 |
|||||
|
3
|
16
|
290
|
5455203667702742753
|
580
|
Jarek
|
|
0,30,44,74,90,120,126,134,156,164,170,200,216,246,260,290
0,260,74,246,200,120,126,134,216,44,290,30,164,156,90,170 |
|||||
|
3
|
16
|
290
|
581991362272134047
|
580
|
Jarek
|
|
0,24,60,80,84,104,126,140,150,164,186,206,210,230,266,290
0,266,104,210,230,84,126,140,186,80,290,24,164,150,60,206 |
|||||
|
3
|
16
|
290
|
7049872471938858473
|
580
|
Jarek
|
|
0,60,66,74,90,126,134,140,150,156,164,200,216,224,230,290
0,230,134,216,224,126,90,140,156,74,290,60,200,150,66,164 |
|||||
|
3
|
16
|
292
|
2206032236894340637
|
584
|
Jarek
|
|
0,6,66,70,72,76,136,142,150,156,216,220,222,226,286,292
0,286,76,222,226,72,150,136,216,70,292,6,142,156,66,220 |
|||||
|
3
|
16
|
296
|
1922678141706492617
|
592
|
Jarek
|
|
0,14,30,44,96,110,126,140,156,170,186,200,252,266,282,296
0,266,44,282,200,126,156,110,252,14,296,30,140,186,96,170 |
|||||
|
3
|
16
|
296
|
3300491071530767057
|
592
|
Jarek
|
|
0,6,20,26,126,132,144,146,150,152,164,170,270,276,290,296
0,290,26,276,170,132,144,146,270,20,296,6,152,150,126,164 |
|||||
|
3
|
16
|
296
|
35384185528375907
|
592
|
Jarek
|
|
0,26,60,84,86,110,126,144,152,170,186,210,212,236,270,296
0,236,86,270,212,144,126,110,210,26,296,60,170,186,84,152 |
|||||
|
3
|
16
|
296
|
5882949102848933627
|
592
|
Jarek
|
|
0,30,42,72,110,114,140,144,152,156,182,186,224,254,266,296
0,266,140,186,254,72,114,152,156,110,296,30,182,144,42,224 |
|||||
|
3
|
16
|
296
|
6515642224149647357
|
592
|
Jarek
|
|
0,14,30,44,96,110,126,140,156,170,186,200,252,266,282,296
0,266,44,282,200,126,156,110,252,14,296,30,140,186,96,170 |
|||||
|
3
|
16
|
296
|
6583373692724467757
|
592
|
Jarek
|
|
0,30,56,66,86,96,122,144,152,174,200,210,230,240,266,296
0,266,86,240,230,96,144,122,210,56,296,30,152,174,66,200 |
|||||
|
3
|
16
|
296
|
7102186209897030767
|
592
|
Jarek
|
|
0,42,50,60,92,102,110,144,152,186,194,204,236,246,254,296
0,254,92,246,236,102,144,110,204,50,296,42,152,186,60,194 |
|||||
|
3
|
16
|
296
|
7404329590632669491
|
592
|
Jarek
|
|
0,18,38,56,90,108,128,146,150,168,188,206,240,258,278,296
0,278,56,258,206,108,150,128,240,38,296,18,146,168,90,188 |
|||||
|
3
|
16
|
296
|
839844930382762247
|
592
|
Jarek
|
|
0,54,60,72,110,114,126,132,164,170,182,186,224,236,242,296
0,242,164,186,236,114,72,170,132,110,296,54,224,126,60,182 |
|||||
|
3
|
16
|
298
|
117243928896938071
|
596
|
Jarek
|
|
0,16,30,46,96,112,126,142,156,172,186,202,252,268,282,298
0,268,46,282,202,126,156,112,252,16,298,30,142,186,96,172 |
|||||
|
3
|
16
|
298
|
2071769060449445971
|
596
|
Jarek
|
|
0,60,66,70,102,126,130,136,162,168,172,196,228,232,238,298
0,238,130,228,232,126,102,136,168,70,298,60,196,162,66,172 |
|||||
|
3
|
16
|
298
|
266628508388015611
|
596
|
Jarek
|
|
0,6,22,28,60,66,82,88,210,216,232,238,270,276,292,298
0,292,28,276,238,66,210,82,270,22,298,6,88,216,60,232 |
|||||
|
3
|
16
|
298
|
4319730598361536231
|
596
|
Jarek
|
|
0,18,42,58,60,76,100,118,180,198,222,238,240,256,280,298
0,280,76,240,256,60,180,100,222,58,298,18,118,198,42,238 |
|||||
|
3
|
16
|
298
|
5797097809523551351
|
596
|
Jarek
|
|
0,28,72,78,100,106,120,148,150,178,192,198,220,226,270,298
0,226,100,270,220,150,120,106,198,28,298,72,178,192,78,148 |
|||||
|
3
|
16
|
298
|
6092270314536820741
|
596
|
Jarek
|
|
0,12,48,60,78,90,126,138,160,172,208,220,238,250,286,298
0,286,172,138,250,60,78,208,126,160,298,12,220,90,48,238 |
|||||
|
3
|
16
|
302
|
4298579701630856771
|
604
|
Jarek
|
|
0,12,30,42,110,122,140,150,152,162,180,192,260,272,290,302
0,290,122,192,272,42,150,140,180,110,302,12,152,162,30,260 |
|||||
|
3
|
16
|
302
|
4996547000548290659
|
604
|
Jarek
|
|
0,8,42,50,120,128,132,140,162,170,174,182,252,260,294,302
0,260,50,294,182,162,132,128,252,8,302,42,170,174,120,140 |
|||||
|
3
|
16
|
302
|
6520120848596434049
|
604
|
Jarek
|
|
0,18,42,50,60,68,92,110,192,210,234,242,252,260,284,302
0,284,68,252,260,60,192,92,234,50,302,18,110,210,42,242 |
|||||
|
3
|
16
|
302
|
7047060358716199097
|
604
|
Jarek
|
|
0,26,30,56,66,92,96,122,180,206,210,236,246,272,276,302
0,272,56,276,236,96,180,92,246,26,302,30,122,210,66,206 |
|||||
|
3
|
16
|
302
|
7214261446565240399
|
604
|
Jarek
|
|
0,2,48,50,120,122,132,134,168,170,180,182,252,254,300,302
0,254,50,300,182,168,132,122,252,2,302,48,170,180,120,134 |
|||||
|
3
|
16
|
304
|
2046668965721502079
|
608
|
Jarek
|
|
0,42,60,70,102,112,130,132,172,174,192,202,234,244,262,304
0,262,112,234,244,102,132,130,192,70,304,42,172,174,60,202 |
|||||
|
3
|
16
|
304
|
3477773609348442967
|
608
|
Jarek
|
|
0,30,40,70,84,114,124,150,154,180,190,220,234,264,274,304
0,274,70,264,220,114,150,124,234,40,304,30,154,180,84,190 |
|||||
|
3
|
16
|
304
|
4009988039455789603
|
608
|
Jarek
|
|
0,18,60,70,78,88,130,148,156,174,216,226,234,244,286,304
0,286,88,234,244,78,156,130,216,70,304,18,148,174,60,226 |
|||||
|
3
|
16
|
304
|
5266069044156294013
|
608
|
Jarek
|
|
0,30,54,70,84,100,124,150,154,180,204,220,234,250,274,304
0,274,100,234,250,84,150,124,204,70,304,30,154,180,54,220 |
|||||
|
3
|
16
|
304
|
994431411078636463
|
608
|
Jarek
|
|
0,18,30,48,70,88,100,118,186,204,216,234,256,274,286,304
0,286,88,234,274,48,186,100,216,70,304,18,118,204,30,256 |
|||||
|
3
|
16
|
310
|
1249673986036931797
|
620
|
Jarek
|
|
0,6,60,66,84,90,144,150,160,166,220,226,244,250,304,310
0,304,166,150,250,66,84,220,144,160,310,6,226,90,60,244 |
|||||
|
3
|
16
|
310
|
1810044612251839399
|
620
|
Jarek
|
|
0,22,30,52,90,112,120,142,168,190,198,220,258,280,288,310
0,280,52,288,220,120,168,112,258,22,310,30,142,198,90,190 |
|||||
|
3
|
16
|
310
|
6335241952834452079
|
620
|
Jarek
|
|
0,10,42,48,52,58,90,100,210,220,252,258,262,268,300,310
0,268,52,300,262,90,210,58,258,10,310,42,100,252,48,220 |
|||||
|
3
|
16
|
312
|
4151299905250340849
|
624
|
Jarek
|
|
0,12,30,42,102,114,132,144,168,180,198,210,270,282,300,312
0,282,42,300,210,132,168,114,270,12,312,30,144,198,102,180 |
|||||
|
3
|
16
|
314
|
1133184478443607433
|
628
|
Jarek
|
|
0,6,20,26,78,84,98,104,210,216,230,236,288,294,308,314
0,308,26,294,236,84,210,98,288,20,314,6,104,216,78,230 |
|||||
|
3
|
16
|
314
|
1171794689385255863
|
628
|
Jarek
|
|
0,30,48,78,96,126,140,144,170,174,188,218,236,266,284,314
0,284,170,174,266,78,96,188,144,140,314,30,218,126,48,236 |
|||||
|
3
|
16
|
314
|
471417195780846839
|
628
|
Jarek
|
|
0,42,60,80,102,122,132,140,174,182,192,212,234,254,272,314
0,272,122,234,254,102,132,140,192,80,314,42,182,174,60,212 |
|||||
|
3
|
16
|
314
|
6396245042791103567
|
628
|
Jarek
|
|
0,42,72,90,110,114,132,152,162,182,200,204,224,242,272,314
0,272,152,204,242,114,90,182,162,110,314,42,224,132,72,200 |
|||||
|
3
|
16
|
314
|
6405764357124778559
|
628
|
Jarek
|
|
0,30,42,72,102,132,140,144,170,174,182,212,242,272,284,314
0,284,170,174,272,72,102,182,144,140,314,30,212,132,42,242 |
|||||
|
3
|
16
|
316
|
102543159231677887
|
632
|
Jarek
|
|
0,30,46,76,84,114,130,156,160,186,202,232,240,270,286,316
0,286,76,270,232,114,156,130,240,46,316,30,160,186,84,202 |
|||||
|
3
|
16
|
316
|
437180789975621413
|
632
|
Jarek
|
|
0,18,28,46,60,78,88,106,210,228,238,256,270,288,298,316
0,298,46,288,256,78,210,88,270,28,316,18,106,228,60,238 |
|||||
|
3
|
16
|
316
|
471298937749607257
|
632
|
Jarek
|
|
0,24,30,42,54,66,72,96,220,244,250,262,274,286,292,316
0,292,244,96,286,54,42,250,72,220,316,24,274,66,30,262 |
|||||
|
3
|
16
|
316
|
656718384132837967
|
632
|
Jarek
|
|
0,24,70,72,94,96,142,150,166,174,220,222,244,246,292,316
0,292,94,246,244,96,150,142,222,70,316,24,166,174,72,220 |
|||||
|
3
|
16
|
320
|
1151506862162394281
|
640
|
Jarek
|
|
0,20,42,62,78,98,120,140,180,200,222,242,258,278,300,320
0,278,62,300,242,120,180,98,258,20,320,42,140,222,78,200 |
|||||
|
3
|
16
|
320
|
4071507019363633589
|
640
|
Jarek
|
|
0,42,78,90,110,120,132,152,168,188,200,210,230,242,278,320
0,278,152,210,242,120,90,188,168,110,320,42,230,132,78,200 |
|||||
|
3
|
16
|
320
|
5710290893708538971
|
640
|
Jarek
|
|
0,12,30,42,80,92,110,122,198,210,228,240,278,290,308,320
0,308,92,240,290,42,198,110,228,80,320,12,122,210,30,278 |
|||||
|
3
|
16
|
322
|
1372774196925859801
|
644
|
Jarek
|
|
0,6,30,36,126,132,156,160,162,166,190,196,286,292,316,322
0,316,166,162,292,36,126,190,156,160,322,6,196,132,30,286 |
|||||
|
3
|
16
|
322
|
4547410142449237069
|
644
|
Jarek
|
|
0,30,70,84,100,114,138,154,168,184,208,222,238,252,292,322
0,292,100,252,238,114,138,154,222,70,322,30,184,168,84,208 |
|||||
|
3
|
16
|
322
|
53517627231758089
|
644
|
Jarek
|
|
0,30,70,100,108,114,138,144,178,184,208,214,222,252,292,322
0,292,100,252,214,138,114,178,222,70,322,30,208,144,108,184 |
|||||
|
3
|
16
|
322
|
78083002410887917
|
644
|
Jarek
|
|
0,46,60,66,106,112,126,150,172,196,210,216,256,262,276,322
0,262,106,276,256,126,150,112,216,46,322,60,172,210,66,196 |
|||||
|
3
|
16
|
326
|
7227342547726952747
|
652
|
Jarek
|
|
0,24,66,90,116,120,140,144,182,186,206,210,236,260,302,326
0,302,140,210,260,90,120,182,186,116,326,24,206,144,66,236 |
|||||
|
3
|
16
|
328
|
1447873525247482441
|
656
|
Jarek
|
|
0,10,42,52,66,76,108,118,210,220,252,262,276,286,318,328
0,286,52,318,262,108,210,76,276,10,328,42,118,252,66,220 |
|||||
|
3
|
16
|
328
|
4563371727471654439
|
656
|
Jarek
|
|
0,24,70,90,94,114,144,160,168,184,214,234,238,258,304,328
0,304,94,258,238,114,144,160,234,70,328,24,184,168,90,214 |
|||||
|
3
|
16
|
328
|
5088634411611680821
|
656
|
Jarek
|
|
0,12,40,52,126,138,150,162,166,178,190,202,276,288,316,328
0,316,52,288,202,138,150,166,276,40,328,12,178,162,126,190 |
|||||
|
3
|
16
|
332
|
3636409035415400477
|
664
|
Jarek
|
|
0,56,60,90,116,126,146,150,182,186,206,216,242,272,276,332
0,272,116,276,242,150,126,146,216,56,332,60,206,186,90,182 |
|||||
|
3
|
16
|
332
|
6868687010299798889
|
664
|
Jarek
|
|
0,2,60,62,102,104,162,164,168,170,228,230,270,272,330,332
0,272,62,330,230,162,168,104,270,2,332,60,164,228,102,170 |
|||||
|
3
|
16
|
334
|
5561040821824457257
|
668
|
Jarek
|
|
0,22,30,52,120,142,150,162,172,184,192,214,282,304,312,334
0,304,52,312,214,150,162,142,282,22,334,30,172,192,120,184 |
|||||
|
3
|
16
|
338
|
2443098533675855513
|
676
|
Jarek
|
|
0,20,30,50,78,98,108,128,210,230,240,260,288,308,318,338
0,308,50,318,260,108,210,98,288,20,338,30,128,240,78,230 |
|||||
|
3
|
16
|
338
|
4281439550083215131
|
676
|
Jarek
|
|
0,8,42,50,78,86,120,128,210,218,252,260,288,296,330,338
0,296,50,330,260,120,210,86,288,8,338,42,128,252,78,218 |
|||||
|
3
|
16
|
338
|
5095550974094646059
|
676
|
Jarek
|
|
0,14,30,44,114,128,144,158,180,194,210,224,294,308,324,338
0,308,44,324,224,144,180,128,294,14,338,30,158,210,114,194 |
|||||
|
3
|
16
|
338
|
5360825217429203801
|
676
|
Jarek
|
|
0,42,60,96,102,138,140,156,182,198,200,236,242,278,296,338
0,296,182,198,278,102,96,200,156,140,338,42,242,138,60,236 |
|||||
|
3
|
16
|
338
|
6265903759874222141
|
676
|
Jarek
|
|
0,56,60,66,116,122,126,156,182,212,216,222,272,278,282,338
0,278,116,282,272,126,156,122,222,56,338,60,182,216,66,212 |
|||||
|
3
|
16
|
338
|
6807902690803755911
|
676
|
Jarek
|
|
0,18,38,56,90,108,128,146,192,210,230,248,282,300,320,338
0,320,56,300,248,108,192,128,282,38,338,18,146,210,90,230 |
|||||
|
3
|
16
|
338
|
7085130922363496141
|
676
|
Jarek
|
|
0,38,42,80,90,128,132,168,170,206,210,248,258,296,300,338
0,296,80,300,248,132,168,128,258,38,338,42,170,210,90,206 |
|||||
|
3
|
16
|
340
|
2465521514662779829
|
680
|
Jarek
|
|
0,60,70,72,130,132,138,142,198,202,208,210,268,270,280,340
0,280,130,270,268,132,138,142,210,70,340,60,202,198,72,208 |
|||||
|
3
|
16
|
340
|
500155744849852957
|
680
|
Jarek
|
|
0,24,66,90,120,130,144,154,186,196,210,220,250,274,316,340
0,316,154,210,274,90,120,196,186,130,340,24,220,144,66,250 |
|||||
|
3
|
16
|
340
|
580958830135976893
|
680
|
Jarek
|
|
0,30,54,84,100,130,154,156,184,186,210,240,256,286,310,340
0,310,130,240,286,84,156,154,210,100,340,30,184,186,54,256 |
|||||
|
3
|
16
|
344
|
4340182020207507953
|
688
|
Jarek
|
|
0,48,50,90,98,138,140,156,188,204,206,246,254,294,296,344
0,296,98,294,254,138,156,140,246,50,344,48,188,204,90,206 |
|||||
|
3
|
16
|
346
|
3038165674182487351
|
692
|
Jarek
|
|
0,18,48,66,70,88,118,136,210,228,258,276,280,298,328,346
0,328,88,276,298,66,210,118,258,70,346,18,136,228,48,280 |
|||||
|
3
|
16
|
346
|
4446407233901388037
|
692
|
Jarek
|
|
0,6,66,72,84,90,150,156,190,196,256,262,274,280,340,346
0,340,196,156,280,72,84,256,150,190,346,6,262,90,66,274 |
|||||
|
3
|
16
|
346
|
4651594019187640867
|
692
|
Jarek
|
|
0,42,70,102,112,132,144,172,174,202,214,234,244,276,304,346
0,304,112,276,244,144,132,172,234,70,346,42,214,174,102,202 |
|||||
|
3
|
16
|
352
|
2326497647118740959
|
704
|
Jarek
|
|
0,48,70,114,118,120,162,168,184,190,232,234,238,282,304,352
0,304,118,282,238,162,120,184,234,70,352,48,232,168,114,190 |
|||||
|
3
|
16
|
352
|
4970537363787854701
|
704
|
Jarek
|
|
0,30,36,66,126,156,160,162,190,192,196,226,286,316,322,352
0,322,190,192,316,66,126,196,162,160,352,30,226,156,36,286 |
|||||
|
3
|
16
|
352
|
6142863083364710359
|
704
|
Jarek
|
|
0,18,70,72,88,90,142,160,192,210,262,264,280,282,334,352
0,334,88,282,280,90,192,142,264,70,352,18,160,210,72,262 |
|||||
|
3
|
16
|
356
|
1153390150252542617
|
712
|
Jarek
|
|
0,24,60,84,90,114,150,174,182,206,242,266,272,296,332,356
0,332,206,174,296,84,90,242,150,182,356,24,266,114,60,272 |
|||||
|
3
|
16
|
356
|
1790884813919768417
|
712
|
Jarek
|
|
0,36,56,90,92,126,146,174,182,210,230,264,266,300,320,356
0,320,92,300,266,126,174,146,264,56,356,36,182,210,90,230 |
|||||
|
3
|
16
|
356
|
4088942087717211827
|
712
|
Jarek
|
|
0,12,60,72,114,126,170,174,182,186,230,242,284,296,344,356
0,344,182,186,296,72,114,230,174,170,356,12,242,126,60,284 |
|||||
|
3
|
16
|
358
|
2639259096347485153
|
716
|
Jarek
|
|
0,24,34,58,90,114,124,148,210,234,244,268,300,324,334,358
0,334,58,324,268,114,210,124,300,34,358,24,148,234,90,244 |
|||||
|
3
|
16
|
358
|
3565892726219917759
|
716
|
Jarek
|
|
0,54,70,84,124,138,150,154,204,208,220,234,274,288,304,358
0,304,124,288,274,138,150,154,234,70,358,54,208,204,84,220 |
|||||
|
3
|
16
|
358
|
904317321628148641
|
716
|
Jarek
|
|
0,6,30,36,126,132,156,162,196,202,226,232,322,328,352,358
0,352,202,162,328,36,126,226,156,196,358,6,232,132,30,322 |
|||||
(*) magic costant=prime*4+magic
Here are the best solution arrived after the ending of the competition:
|
Task
|
K-tuple
|
Diameter
|
Prime
|
Magic(*)
|
Name
|
|---|
(*) magic costant=prime*4+magic
Ranking for K-Tuples of Primes
This is the Ranking of the K-Tuples of Primes competition:
|
Pos
|
User
|
Points
|
T1
|
T2
|
T3
|
Last Improvement
|
|---|---|---|---|---|---|---|
|
1
|
Jarek
|
368
|
29
|
5
|
334
|
17/11/2015
|
|
2
|
Natalia Makarova
|
5
|
4
|
1
|
02/10/2015
|
Primes k-tuple
Competition #4
This competition is organized by Макарова Наталия (Natalia Makarova)
Definitions
Definition 1:
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.
We consider the k-tuple, where p + a1, p + a2, p + a3, …, p + ak are consecutive primes.
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:
a1 + ak = a2 + a[k-1] = a3 + a[k-2] = … = a[k/2] + a[k/2+1]
Example: symmetric 8-tuple
(17 + 0, 17 + 2, 17 + 6, 17 + 12, 17 + 14, 17 + 20, 17 + 24, 17 + 26)
Shortened we write this:
17: 0, 2, 6, 12, 14, 20, 24, 26
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:
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: symmetric 5-tuple
18713: 0, 6, 18, 30, 36
Definition 4:
The diameter d of k-tuple is the difference of its largest and smallest elements.
Example: 8-tuple
17: 0, 2, 6, 12, 14, 20, 24, 26
It has a diameter d = 26.
Definition 5:
A pandiagonal magic square is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the magic constant.
The Contest
In the contest is required to compete for those tasks:
Task 1
Required to find k-tuples with the minimal value p:
for an even k > 24; for odd k > 15.
Example
15-tuple, p=3945769040698829 (minimal) 3945769040698829: 0, 12, 18, 42, 102, 138, 180, 210, 240, 282, 318, 378, 402, 408, 420
Task 2
Required to find k-tuples with a minimal diameter d:
for an even k > 10; for odd k > 13.
Example
8-tuple with a minimal diameter d = 26
17: 0, 2, 6, 12, 14, 20, 24, 26
Task 3
Required to find the 16-tuple, the elements of which it is possible to make pandiagonal magic square of order 4 with magic constant S as: 94615738903617540 < S < 29643562211780078520
Example 16-tuple
23653934725904299: 0, 12, 22, 34, 48, 60, 70, 82, 90, 102, 112, 124, 138, 150, 160, 172
pandiagonal magic square
23653934725904299+ 0 160 60 124 82 102 22 138 112 48 172 12 150 34 90 70 S=94615738903617540
Rule:
Prime numbers can contain no more than 100 digits.
In tasks 1 and 2 k <= 50.
Format of solution
For every task the first line is the number of task you are entering: so 1, 2 or 3. After there are those lines according to the tasks you are inserting.
In tasks 1 and 2
k-tuple is represented as
p: a1, a2, a3, …, ak
Example
18713: 0, 6, 18, 30, 36
In task 3
it is 16-tuple and pandiagonal magic square of order 4, composed of the elements of the tuple.
Example
23653934725904299: 0, 12, 22, 34, 48, 60, 70, 82, 90, 102, 112, 124, 138, 150, 160, 172 0, 160, 60, 124, 82, 102, 22, 138, 112, 48, 172, 12, 150, 34, 90, 70
Scoring
The contestant receives one point for every solution to tasks 1 and 3.
For each k in task 2 one point counted towards only those participants, who will have a minimum diameter d.
The Prize
If two or more contestants have equal number of points, the winner will be the entrant who submitted solutions ahead of other contestants.
The winner will receive a prize of 5,000 rubles.
If the winner is not from Russia, the prize will be paid in US dollars at the official exchange rate on the day ending of the contest.
Thanks
We thanks Wolfram Alpha as we use their API for testing the primality of the given big numbers.
Links
[1] https://en.wikipedia.org/wiki/Prime_k-tuple
[2] https://en.wikipedia.org/wiki/Pandiagonal_magic_square
[3] http://oeis.org/A256234
[4] http://oeis.org/A081235
[5] http://oeis.org/A055380
[6] http://oeis.org/A055382
[7] http://oeis.org/A175309
[8] http://www.primepuzzles.net/problems/prob_060.htm
[9] http://dxdy.ru/topic93581.html
[10] http://dxdy.ru/topic87170.html