Пентадекатлон мечты

[Yadryara]

Dmitriy40 в сообщении #1575061 писал(а):

Забавное наблюдение: все квадраты $10p^2, 14p^2, 15p^2, 21p^2$ встречаются исключительно вместе. Т.е. в цепочках длиной 14+ они присутствуют все,

Ну, собственно, вот они все $1116-1044 = 72$ "квадратных" варианта именно для 14-к:

(72)

1    [9, 10, 11, 12, 13, 14, 15, 32, 1, 18, 1, 20, 21, 22]
2    [9, 10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 22]
3    [9, 10, 11, 12, 371293, 14, 15, 32, 1, 18, 1, 20, 21, 22]
4    [9, 10, 11, 12, 2197, 14, 15, 32, 1, 18, 1, 20, 21, 22]
5    [9, 10, 11, 12, 13, 14, 15, 32, 1, 18, 1, 20, 21, 242]
6    [9, 10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 242]
7    [9, 10, 11, 12, 371293, 14, 15, 32, 1, 18, 1, 20, 21, 242]
8    [9, 10, 11, 12, 2197, 14, 15, 32, 1, 18, 1, 20, 21, 242]
9    [45, 2, 11, 12, 7, 50, 3, 32, 1, 18, 5, 28, 507, 22]
10    [45, 2, 11, 12, 7, 50, 3, 32, 1, 18, 845, 28, 3, 22]
11    [45, 2, 11, 12, 1183, 50, 3, 32, 1, 18, 5, 28, 3, 22]
12    [45, 338, 11, 12, 7, 50, 3, 32, 1, 18, 5, 28, 3, 22]
13    [45, 2, 11, 12, 637, 50, 3, 32, 1, 18, 5, 28, 3, 22]
14    [45, 2, 11, 12, 49, 50, 3, 32, 1, 18, 5, 28, 507, 22]
15    [45, 2, 11, 12, 49, 50, 3, 32, 1, 18, 845, 28, 3, 22]
16    [45, 338, 11, 12, 49, 50, 3, 32, 1, 18, 5, 28, 3, 22]
17    [45, 2, 11, 12, 16807, 50, 3, 32, 1, 18, 5, 28, 507, 22]
18    [45, 2, 11, 12, 16807, 50, 3, 32, 1, 18, 845, 28, 3, 22]
19    [45, 338, 11, 12, 16807, 50, 3, 32, 1, 18, 5, 28, 3, 22]
20    [1, 2, 3, 4, 5, 18, 7, 32, 3, 50, 11, 12, 2197, 98]
21    [1, 2, 3, 4, 5, 18, 7, 32, 3, 50, 121, 12, 2197, 98]
22    [1, 2, 3, 4, 5, 18, 847, 32, 3, 50, 1, 12, 2197, 98]
23    [1, 2, 3, 4, 605, 18, 7, 32, 3, 50, 1, 12, 2197, 98]
24    [1, 2, 3, 4, 5, 18, 7, 32, 3, 50, 161051, 12, 2197, 98]
25    [1, 2, 3, 4, 5, 18, 7, 32, 3, 50, 1331, 12, 13, 98]
26    [1, 2, 3, 52, 5, 18, 7, 32, 3, 50, 1331, 12, 1, 98]
27    [1, 2, 3, 4, 5, 18, 7, 32, 3, 50, 1331, 12, 169, 98]
28    [1, 2, 3, 4, 5, 18, 7, 32, 507, 50, 1331, 12, 1, 98]
29    [1, 2, 3, 4, 845, 18, 7, 32, 3, 50, 1331, 12, 1, 98]
30    [1, 2, 507, 4, 5, 18, 7, 32, 3, 50, 1331, 12, 1, 98]
31    [1, 2, 3, 4, 5, 18, 7, 32, 3, 50, 1331, 12, 371293, 98]
32    [1, 2, 3, 4, 5, 18, 7, 32, 3, 50, 1331, 12, 2197, 98]
33    [243, 10, 11, 12, 13, 14, 15, 32, 1, 18, 1, 20, 21, 22]
34    [243, 10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 22]
35    [243, 10, 11, 12, 371293, 14, 15, 32, 1, 18, 1, 20, 21, 22]
36    [243, 10, 11, 12, 2197, 14, 15, 32, 1, 18, 1, 20, 21, 22]
37    [243, 10, 11, 12, 13, 14, 15, 32, 1, 18, 1, 20, 21, 242]
38    [243, 10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 242]
39    [243, 10, 11, 12, 371293, 14, 15, 32, 1, 18, 1, 20, 21, 242]
40    [243, 10, 11, 12, 2197, 14, 15, 32, 1, 18, 1, 20, 21, 242]
41    [10, 11, 12, 13, 14, 15, 32, 1, 18, 1, 20, 21, 22, 1]
42    [10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 22, 1]
43    [10, 11, 12, 371293, 14, 15, 32, 1, 18, 1, 20, 21, 22, 1]
44    [10, 11, 12, 2197, 14, 15, 32, 1, 18, 1, 20, 21, 22, 1]
45    [10, 11, 12, 13, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]
46    [10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]
47    [10, 11, 12, 371293, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]
48    [10, 11, 12, 2197, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]
49    [2, 11, 12, 7, 50, 3, 32, 1, 18, 5, 28, 507, 22, 1]
50    [2, 11, 12, 7, 50, 3, 32, 1, 18, 845, 28, 3, 22, 1]
51    [2, 11, 12, 1183, 50, 3, 32, 1, 18, 5, 28, 3, 22, 1]
52    [338, 11, 12, 7, 50, 3, 32, 1, 18, 5, 28, 3, 22, 13]
53    [2, 11, 12, 637, 50, 3, 32, 1, 18, 5, 28, 3, 22, 1]
54    [2, 11, 12, 49, 50, 3, 32, 1, 18, 5, 28, 507, 22, 1]
55    [2, 11, 12, 49, 50, 3, 32, 1, 18, 845, 28, 3, 22, 1]
56    [338, 11, 12, 49, 50, 3, 32, 1, 18, 5, 28, 3, 22, 13]
57    [2, 11, 12, 16807, 50, 3, 32, 1, 18, 5, 28, 507, 22, 1]
58    [2, 11, 12, 16807, 50, 3, 32, 1, 18, 845, 28, 3, 22, 1]
59    [338, 11, 12, 16807, 50, 3, 32, 1, 18, 5, 28, 3, 22, 13]
60    [2, 3, 4, 5, 18, 7, 32, 3, 50, 11, 12, 2197, 98, 45]
61    [2, 3, 4, 5, 18, 7, 32, 3, 50, 121, 12, 2197, 98, 45]
62    [2, 3, 4, 5, 18, 847, 32, 3, 50, 1, 12, 2197, 98, 45]
63    [2, 3, 4, 605, 18, 7, 32, 3, 50, 1, 12, 2197, 98, 45]
64    [2, 3, 4, 5, 18, 7, 32, 3, 50, 161051, 12, 2197, 98, 45]
65    [2, 3, 4, 5, 18, 7, 32, 3, 50, 1331, 12, 13, 98, 45]
66    [2, 3, 52, 5, 18, 7, 32, 3, 50, 1331, 12, 1, 98, 45]
67    [2, 3, 4, 5, 18, 7, 32, 3, 50, 1331, 12, 169, 98, 45]
68    [2, 3, 4, 5, 18, 7, 32, 507, 50, 1331, 12, 1, 98, 45]
69    [2, 3, 4, 845, 18, 7, 32, 3, 50, 1331, 12, 1, 98, 45]
70    [2, 507, 4, 5, 18, 7, 32, 3, 50, 1331, 12, 1, 98, 45]
71    [2, 3, 4, 5, 18, 7, 32, 3, 50, 1331, 12, 371293, 98, 45]
72    [2, 3, 4, 5, 18, 7, 32, 3, 50, 1331, 12, 2197, 98, 45]

Да, 24 из них содержат именно эти 4 вида чисел.

[Yadryara]

EUgeneUS в сообщении #1574466 писал(а):

1. Количество проверяемых мест (больших простых) до расстановки квадратов бывает от 5 до 9.

4 CP(Checked Place) тоже бывает. Вот расклад по всем паттернам для 14-к:

CP   Patterns

4           6
5          40
6         259
7         484
8         285
9          42
_____________
         1116

Ну а вот и та самая 6-ка:

   9,  10,  11,    12,    13,  14,  15,  32,   1,  18,   1,  20,  21,  22;
   9,  10,  11,    12,   169,  14,  15,  32,   1,  18,   1,  20,  21,  22;
   9,  10,  11,    12,  2197,  14,  15,  32,   1,  18,   1,  20,  21,  22;
  10,  11,  12,    13,    14,  15,  32,   1,  18,   1,  20,  21,  22,   1;
  10,  11,  12,   169,    14,  15,  32,   1,  18,   1,  20,  21,  22,   1;
  10,  11,  12,  2197,    14,  15,  32,   1,  18,   1,  20,  21,  22,   1;

[Yadryara]

EUgeneUS в сообщении #1574513 писал(а):

2. The smallest number $p$ after squaring primes for D(12,14) is $10$. And it is achieved only in 78 patterns.

Ну полный список всё-таки состоит из 82-х паттернов, в которых после полного заполнения будет 10 CP.

(82)

1  [9, 10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 22]
2  [9, 10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 242]
3  [1, 2, 3, 28, 5, 18, 1, 32, 363, 50, 49, 12, 169, 2]
4  [1, 2, 3, 28, 5, 18, 169, 32, 363, 50, 49, 12, 1, 2]
5  [1, 2, 3, 28, 845, 18, 1, 32, 363, 50, 49, 12, 1, 2]
6  [1, 2, 507, 28, 5, 18, 1, 32, 363, 50, 49, 12, 1, 2]
7  [1, 338, 3, 28, 5, 18, 1, 32, 363, 50, 49, 12, 1, 2]
8  [1, 2, 3, 28, 5, 18, 121, 32, 3, 50, 49, 12, 169, 2]
9  [1, 2, 3, 28, 5, 18, 121, 32, 507, 50, 49, 12, 1, 2]
10  [1, 2, 3, 28, 845, 18, 121, 32, 3, 50, 49, 12, 1, 2]
11  [1, 2, 507, 28, 5, 18, 121, 32, 3, 50, 49, 12, 1, 2]
12  [1, 338, 3, 28, 5, 18, 121, 32, 3, 50, 49, 12, 1, 2]
13  [1, 2, 3, 28, 605, 18, 1, 32, 3, 50, 49, 12, 169, 2]
14  [1, 2, 3, 28, 605, 18, 1, 32, 507, 50, 49, 12, 1, 2]
15  [1, 2, 3, 28, 605, 18, 169, 32, 3, 50, 49, 12, 1, 2]
16  [1, 2, 507, 28, 605, 18, 1, 32, 3, 50, 49, 12, 1, 2]
17  [1, 338, 3, 28, 605, 18, 1, 32, 3, 50, 49, 12, 1, 2]
18  [1, 2, 3, 4, 5, 18, 7, 32, 3, 50, 121, 12, 169, 98]
19  [1, 2, 3, 4, 5, 18, 7, 32, 507, 50, 121, 12, 1, 98]
20  [1, 2, 3, 4, 5, 18, 1183, 32, 3, 50, 121, 12, 1, 98]
21  [1, 2, 3, 4, 845, 18, 7, 32, 3, 50, 121, 12, 1, 98]
22  [1, 2, 507, 4, 5, 18, 7, 32, 3, 50, 121, 12, 1, 98]
23  [1, 338, 3, 4, 5, 18, 7, 32, 3, 50, 121, 12, 1, 98]
24  [1, 2, 3, 4, 5, 18, 7, 32, 363, 50, 1, 12, 169, 98]
25  [1, 2, 3, 4, 5, 18, 7, 32, 363, 50, 169, 12, 1, 98]
26  [1, 2, 3, 4, 5, 18, 1183, 32, 363, 50, 1, 12, 1, 98]
27  [1, 2, 3, 4, 845, 18, 7, 32, 363, 50, 1, 12, 1, 98]
28  [1, 2, 507, 4, 5, 18, 7, 32, 363, 50, 1, 12, 1, 98]
29  [1, 338, 3, 4, 5, 18, 7, 32, 363, 50, 1, 12, 1, 98]
30  [1, 2, 3, 4, 5, 18, 847, 32, 3, 50, 1, 12, 169, 98]
31  [1, 2, 3, 4, 5, 18, 847, 32, 3, 50, 169, 12, 1, 98]
32  [1, 2, 3, 4, 5, 18, 847, 32, 507, 50, 1, 12, 1, 98]
33  [1, 2, 3, 4, 845, 18, 847, 32, 3, 50, 1, 12, 1, 98]
34  [1, 2, 507, 4, 5, 18, 847, 32, 3, 50, 1, 12, 1, 98]
35  [1, 338, 3, 4, 5, 18, 847, 32, 3, 50, 1, 12, 1, 98]
36  [1, 2, 3, 4, 605, 18, 7, 32, 3, 50, 1, 12, 169, 98]
37  [1, 2, 3, 4, 605, 18, 7, 32, 3, 50, 169, 12, 1, 98]
38  [1, 2, 3, 4, 605, 18, 7, 32, 507, 50, 1, 12, 1, 98]
39  [1, 2, 3, 4, 605, 18, 1183, 32, 3, 50, 1, 12, 1, 98]
40  [1, 2, 507, 4, 605, 18, 7, 32, 3, 50, 1, 12, 1, 98]
41  [1, 338, 3, 4, 605, 18, 7, 32, 3, 50, 1, 12, 1, 98]
42  [10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 22, 1]
43  [10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]
44  [98, 1, 12, 1, 50, 3, 32, 7, 18, 605, 4, 3, 338, 1]
45  [98, 1, 12, 1, 50, 3, 32, 7, 18, 605, 4, 507, 2, 1]
46  [98, 1, 12, 1, 50, 3, 32, 1183, 18, 605, 4, 3, 2, 1]
47  [98, 1, 12, 1, 50, 507, 32, 7, 18, 605, 4, 3, 2, 1]
48  [98, 1, 12, 169, 50, 3, 32, 7, 18, 605, 4, 3, 2, 1]
49  [98, 169, 12, 1, 50, 3, 32, 7, 18, 605, 4, 3, 2, 1]
50  [98, 1, 12, 1, 50, 3, 32, 847, 18, 5, 4, 3, 338, 1]
51  [98, 1, 12, 1, 50, 3, 32, 847, 18, 5, 4, 507, 2, 1]
52  [98, 1, 12, 1, 50, 3, 32, 847, 18, 845, 4, 3, 2, 1]
53  [98, 1, 12, 1, 50, 507, 32, 847, 18, 5, 4, 3, 2, 1]
54  [98, 1, 12, 169, 50, 3, 32, 847, 18, 5, 4, 3, 2, 1]
55  [98, 169, 12, 1, 50, 3, 32, 847, 18, 5, 4, 3, 2, 1]
56  [98, 1, 12, 1, 50, 363, 32, 7, 18, 5, 4, 3, 338, 1]
57  [98, 1, 12, 1, 50, 363, 32, 7, 18, 5, 4, 507, 2, 1]
58  [98, 1, 12, 1, 50, 363, 32, 7, 18, 845, 4, 3, 2, 1]
59  [98, 1, 12, 1, 50, 363, 32, 1183, 18, 5, 4, 3, 2, 1]
60  [98, 1, 12, 169, 50, 363, 32, 7, 18, 5, 4, 3, 2, 1]
61  [98, 169, 12, 1, 50, 363, 32, 7, 18, 5, 4, 3, 2, 1]
62  [98, 1, 12, 121, 50, 3, 32, 7, 18, 5, 4, 3, 338, 1]
63  [98, 1, 12, 121, 50, 3, 32, 7, 18, 5, 4, 507, 2, 1]
64  [98, 1, 12, 121, 50, 3, 32, 7, 18, 845, 4, 3, 2, 1]
65  [98, 1, 12, 121, 50, 3, 32, 1183, 18, 5, 4, 3, 2, 1]
66  [98, 1, 12, 121, 50, 507, 32, 7, 18, 5, 4, 3, 2, 1]
67  [98, 169, 12, 121, 50, 3, 32, 7, 18, 5, 4, 3, 2, 1]
68  [2, 1, 12, 49, 50, 3, 32, 1, 18, 605, 28, 3, 338, 1]
69  [2, 1, 12, 49, 50, 3, 32, 1, 18, 605, 28, 507, 2, 1]
70  [2, 1, 12, 49, 50, 3, 32, 169, 18, 605, 28, 3, 2, 1]
71  [2, 1, 12, 49, 50, 507, 32, 1, 18, 605, 28, 3, 2, 1]
72  [2, 169, 12, 49, 50, 3, 32, 1, 18, 605, 28, 3, 2, 1]
73  [2, 1, 12, 49, 50, 3, 32, 121, 18, 5, 28, 3, 338, 1]
74  [2, 1, 12, 49, 50, 3, 32, 121, 18, 5, 28, 507, 2, 1]
75  [2, 1, 12, 49, 50, 3, 32, 121, 18, 845, 28, 3, 2, 1]
76  [2, 1, 12, 49, 50, 507, 32, 121, 18, 5, 28, 3, 2, 1]
77  [2, 169, 12, 49, 50, 3, 32, 121, 18, 5, 28, 3, 2, 1]
78  [2, 1, 12, 49, 50, 363, 32, 1, 18, 5, 28, 3, 338, 1]
79  [2, 1, 12, 49, 50, 363, 32, 1, 18, 5, 28, 507, 2, 1]
80  [2, 1, 12, 49, 50, 363, 32, 1, 18, 845, 28, 3, 2, 1]
81  [2, 1, 12, 49, 50, 363, 32, 169, 18, 5, 28, 3, 2, 1]
82  [2, 169, 12, 49, 50, 363, 32, 1, 18, 5, 28, 3, 2, 1]

[Dmitriy40]

Yadryara в сообщении #1575079 писал(а):

EUgeneUS в сообщении #1574466 писал(а):

1. Количество проверяемых мест (больших простых) до расстановки квадратов бывает от 5 до 9.

4 CP(Checked Place) тоже бывает.
...
Ну а вот и та самая 6-ка:

Цитата была про паттерны без квадратов. И там CP=4 не бывает.

[Yadryara]

Dmitriy40 в сообщении #1575093 писал(а):

Цитата была про паттерны без квадратов. И там CP=4 не бывает.

Я в курсе.

EUgeneUS в сообщении #1574466 писал(а):

11 простых (после подстановки квадратов): всего 316 групп (b*).

Тоже побольше: 339 паттернов.

А общий расклад после полной подстановки квадратов простых такой:

CP    Patterns

10          82
11         339
12         449
13         222
14          24
______________
          1116

[Yadryara]

VAL в сообщении #1560075 писал(а):

Yadryara в сообщении #1560074 писал(а):

А возможны ли паттерны для 12-15 где меньше 11-ти одиночных искомых простых ?

По-видимому, нет.
Мы, вроде бы, это доказали.
"Вроде бы" - поскольку за давностью точно не помню.

Да, нашлись-таки два паттерна для 15-шки, где всего лишь 10 одиночных искомых простых ! Или, в современной терминологии 10 CP :

1  [9, 10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21,  22, 1]
2  [9, 10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]

Ну и всего лишь 72 паттерна с 11 CP, в которые входят и наши знаменитые 64. Они выделены в серединке. 64 группы по 720 это и есть знаменитый стандартный комплект — 46080 паттернов.

(72)

1  [9, 10, 11, 12, 13, 14, 15, 32, 1, 18, 1, 20, 21, 22, 1]
2  [9, 10, 11, 12, 371293, 14, 15, 32, 1, 18, 1, 20, 21, 22, 1]
3  [9, 10, 11, 12, 2197, 14, 15, 32, 1, 18, 1, 20, 21, 22, 1]
4  [9, 10, 11, 12, 13, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]
5  [9, 10, 11, 12, 371293, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]
6  [9, 10, 11, 12, 2197, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]

7  [45, 98, 1, 12, 1, 50, 3, 32, 7, 18, 605, 4, 507, 2, 1]
8  [45, 98, 1, 12, 1, 50, 3, 32, 1183, 18, 605, 4, 3, 2, 1]
9  [45, 98, 1, 12, 1, 50, 507, 32, 7, 18, 605, 4, 3, 2, 1]
10  [45, 98, 1, 12, 169, 50, 3, 32, 7, 18, 605, 4, 3, 2, 1]
11  [45, 98, 169, 12, 1, 50, 3, 32, 7, 18, 605, 4, 3, 2, 1]
12  [45, 98, 1, 12, 1, 50, 3, 32, 847, 18, 5, 4, 507, 2, 1]
13  [45, 98, 1, 12, 1, 50, 3, 32, 847, 18, 845, 4, 3, 2, 1]
14  [45, 98, 1, 12, 1, 50, 507, 32, 847, 18, 5, 4, 3, 2, 1]
15  [45, 98, 1, 12, 169, 50, 3, 32, 847, 18, 5, 4, 3, 2, 1]
16  [45, 98, 169, 12, 1, 50, 3, 32, 847, 18, 5, 4, 3, 2, 1]
17  [45, 98, 1, 12, 1, 50, 363, 32, 7, 18, 5, 4, 507, 2, 1]
18  [45, 98, 1, 12, 1, 50, 363, 32, 7, 18, 845, 4, 3, 2, 1]
19  [45, 98, 1, 12, 1, 50, 363, 32, 1183, 18, 5, 4, 3, 2, 1]
20  [45, 98, 1, 12, 169, 50, 363, 32, 7, 18, 5, 4, 3, 2, 1]
21  [45, 98, 169, 12, 1, 50, 363, 32, 7, 18, 5, 4, 3, 2, 1]
22  [45, 98, 1, 12, 121, 50, 3, 32, 7, 18, 5, 4, 507, 2, 1]
23  [45, 98, 1, 12, 121, 50, 3, 32, 7, 18, 845, 4, 3, 2, 1]
24  [45, 98, 1, 12, 121, 50, 3, 32, 1183, 18, 5, 4, 3, 2, 1]
25  [45, 98, 1, 12, 121, 50, 507, 32, 7, 18, 5, 4, 3, 2, 1]
26  [45, 98, 169, 12, 121, 50, 3, 32, 7, 18, 5, 4, 3, 2, 1]
27  [45, 2, 1, 12, 49, 50, 3, 32, 1, 18, 605, 28, 507, 2, 1]
28  [45, 2, 1, 12, 49, 50, 3, 32, 169, 18, 605, 28, 3, 2, 1]
29  [45, 2, 1, 12, 49, 50, 507, 32, 1, 18, 605, 28, 3, 2, 1]
30  [45, 2, 169, 12, 49, 50, 3, 32, 1, 18, 605, 28, 3, 2, 1]
31  [45, 2, 1, 12, 49, 50, 3, 32, 121, 18, 5, 28, 507, 2, 1]
32  [45, 2, 1, 12, 49, 50, 3, 32, 121, 18, 845, 28, 3, 2, 1]
33  [45, 2, 1, 12, 49, 50, 507, 32, 121, 18, 5, 28, 3, 2, 1]
34  [45, 2, 169, 12, 49, 50, 3, 32, 121, 18, 5, 28, 3, 2, 1]
35  [45, 2, 1, 12, 49, 50, 363, 32, 1, 18, 5, 28, 507, 2, 1]
36  [45, 2, 1, 12, 49, 50, 363, 32, 1, 18, 845, 28, 3, 2, 1]
37  [45, 2, 1, 12, 49, 50, 363, 32, 169, 18, 5, 28, 3, 2, 1]
38  [45, 2, 169, 12, 49, 50, 363, 32, 1, 18, 5, 28, 3, 2, 1]
39  [1, 2, 3, 28, 5, 18, 1, 32, 363, 50, 49, 12, 169, 2, 45]
40  [1, 2, 3, 28, 5, 18, 169, 32, 363, 50, 49, 12, 1, 2, 45]
41  [1, 2, 3, 28, 845, 18, 1, 32, 363, 50, 49, 12, 1, 2, 45]
42  [1, 2, 507, 28, 5, 18, 1, 32, 363, 50, 49, 12, 1, 2, 45]
43  [1, 2, 3, 28, 5, 18, 121, 32, 3, 50, 49, 12, 169, 2, 45]
44  [1, 2, 3, 28, 5, 18, 121, 32, 507, 50, 49, 12, 1, 2, 45]
45  [1, 2, 3, 28, 845, 18, 121, 32, 3, 50, 49, 12, 1, 2, 45]
46  [1, 2, 507, 28, 5, 18, 121, 32, 3, 50, 49, 12, 1, 2, 45]
47  [1, 2, 3, 28, 605, 18, 1, 32, 3, 50, 49, 12, 169, 2, 45]
48  [1, 2, 3, 28, 605, 18, 1, 32, 507, 50, 49, 12, 1, 2, 45]
49  [1, 2, 3, 28, 605, 18, 169, 32, 3, 50, 49, 12, 1, 2, 45]
50  [1, 2, 507, 28, 605, 18, 1, 32, 3, 50, 49, 12, 1, 2, 45]
51  [1, 2, 3, 4, 5, 18, 7, 32, 3, 50, 121, 12, 169, 98, 45]
52  [1, 2, 3, 4, 5, 18, 7, 32, 507, 50, 121, 12, 1, 98, 45]
53  [1, 2, 3, 4, 5, 18, 1183, 32, 3, 50, 121, 12, 1, 98, 45]
54  [1, 2, 3, 4, 845, 18, 7, 32, 3, 50, 121, 12, 1, 98, 45]
55  [1, 2, 507, 4, 5, 18, 7, 32, 3, 50, 121, 12, 1, 98, 45]
56  [1, 2, 3, 4, 5, 18, 7, 32, 363, 50, 1, 12, 169, 98, 45]
57  [1, 2, 3, 4, 5, 18, 7, 32, 363, 50, 169, 12, 1, 98, 45]
58  [1, 2, 3, 4, 5, 18, 1183, 32, 363, 50, 1, 12, 1, 98, 45]
59  [1, 2, 3, 4, 845, 18, 7, 32, 363, 50, 1, 12, 1, 98, 45]
60  [1, 2, 507, 4, 5, 18, 7, 32, 363, 50, 1, 12, 1, 98, 45]
61  [1, 2, 3, 4, 5, 18, 847, 32, 3, 50, 1, 12, 169, 98, 45]
62  [1, 2, 3, 4, 5, 18, 847, 32, 3, 50, 169, 12, 1, 98, 45]
63  [1, 2, 3, 4, 5, 18, 847, 32, 507, 50, 1, 12, 1, 98, 45]
64  [1, 2, 3, 4, 845, 18, 847, 32, 3, 50, 1, 12, 1, 98, 45]
65  [1, 2, 507, 4, 5, 18, 847, 32, 3, 50, 1, 12, 1, 98, 45]
66  [1, 2, 3, 4, 605, 18, 7, 32, 3, 50, 1, 12, 169, 98, 45]
67  [1, 2, 3, 4, 605, 18, 7, 32, 3, 50, 169, 12, 1, 98, 45]
68  [1, 2, 3, 4, 605, 18, 7, 32, 507, 50, 1, 12, 1, 98, 45]
69  [1, 2, 3, 4, 605, 18, 1183, 32, 3, 50, 1, 12, 1, 98, 45]
70  [1, 2, 507, 4, 605, 18, 7, 32, 3, 50, 1, 12, 1, 98, 45]

71  [243, 10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 22, 1]
72  [243, 10, 11, 12, 169, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]

Общий расклад после полной подстановки квадратов простых такой:

CP    Patterns

10           2
11          72
12         223
13         193
14          38
15           0
______________
           528

[Dmitriy40]

Yadryara в сообщении #1575113 писал(а):

Ну и всего лишь 72 паттерна с 11 CP, в которые входят и наши знаменитые 64. Они выделены в серединке. 64 группы по 720 это и есть знаменитый стандартный комплект — 46080 паттернов.

Странно, у меня групп и у Хуго паттернов не 72, а 94 ...

[Yadryara]

Dmitriy40 в сообщении #1575119 писал(а):

Странно, у меня групп и у Хуго паттернов не 72, а 94 ...

$94-64=30$. Покажите эту тридцатку, плиз. А я пока 102 исключённых паттерна проверю.

[Yadryara]

Да, во всех 102-х случаях запрет $15p^2$ по модулю 13 и/или 11.

(102)

1   [9, 10, 1859, 12, 1, 14, 15, 32, 1, 18, 1, 20, 21, 22, 1]       15/13

2   [9, 10, 11, 12, 1, 14, 15, 32, 1, 18, 169, 20, 21, 22, 1]

3   [9, 10, 11, 12, 1, 14, 15, 32, 1, 18, 371293, 20, 21, 22, 1]

4   [9, 10, 11, 12, 1, 14, 15, 32, 1, 18, 13, 20, 21, 22, 1]

5   [9, 10, 169, 12, 121, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

6   [9, 10, 371293, 12, 121, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

7   [9, 10, 13, 12, 121, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]        15/13

8   [9, 10, 1, 12, 1573, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]        15/11

9   [9, 10, 1, 12, 121, 14, 15, 32, 1, 18, 169, 20, 21, 2, 1]

10   [9, 10, 1, 12, 121, 14, 15, 32, 1, 18, 371293, 20, 21, 2, 1]

11   [9, 10, 1, 12, 121, 14, 15, 32, 1, 18, 13, 20, 21, 2, 1]

12   [117, 10, 1, 12, 121, 14, 15, 32, 1, 18, 1, 20, 21, 338, 1]

13   [9, 10, 169, 12, 161051, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

14   [9, 10, 371293, 12, 161051, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

15   [9, 10, 13, 12, 161051, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

16   [9, 10, 1, 12, 161051, 14, 15, 32, 1, 18, 169, 20, 21, 2, 1]

17   [9, 10, 1, 12, 161051, 14, 15, 32, 1, 18, 371293, 20, 21, 2, 1]

18   [9, 10, 1, 12, 161051, 14, 15, 32, 1, 18, 13, 20, 21, 2, 1]

19   [117, 10, 1, 12, 161051, 14, 15, 32, 1, 18, 1, 20, 21, 338, 1]

20   [9, 10, 169, 12, 11, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]       

21   [9, 10, 371293, 12, 11, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

22   [9, 10, 13, 12, 11, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

23   [9, 10, 1, 12, 1859, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

24   [9, 10, 1, 12, 11, 14, 15, 32, 1, 18, 169, 20, 21, 2, 1]

25   [9, 10, 1, 12, 11, 14, 15, 32, 1, 18, 371293, 20, 21, 2, 1]

26   [9, 10, 1, 12, 11, 14, 15, 32, 1, 18, 13, 20, 21, 2, 1]

27   [117, 10, 1, 12, 11, 14, 15, 32, 1, 18, 1, 20, 21, 338, 1]     15/11

28   [9, 10, 169, 12, 1, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]      15/13

29   [9, 10, 371293, 12, 1, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]

30   [9, 10, 13, 12, 1, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]       15/13

31   [9, 10, 1, 12, 169, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]      15/11

32   [9, 10, 1, 12, 371293, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]

33   [9, 10, 1, 12, 13, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]

34   [9, 10, 1, 12, 1, 14, 15, 32, 1, 18, 1573, 20, 21, 2, 1]

35   [117, 10, 1, 12, 1, 14, 15, 32, 1, 18, 121, 20, 21, 338, 1]

36   [9, 10, 169, 12, 1, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

37   [9, 10, 371293, 12, 1, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

38   [9, 10, 13, 12, 1, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

39   [9, 10, 1, 12, 169, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

40   [9, 10, 1, 12, 371293, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

41   [9, 10, 1, 12, 13, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

42   [117, 10, 1, 12, 1, 14, 15, 32, 1, 18, 161051, 20, 21, 338, 1]

43   [9, 10, 169, 12, 1, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]  

44   [9, 10, 371293, 12, 1, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]

45   [9, 10, 13, 12, 1, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]

46   [9, 10, 1, 12, 169, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]

47   [9, 10, 1, 12, 371293, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]

48   [9, 10, 1, 12, 13, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]

49   [9, 10, 1, 12, 1, 14, 15, 32, 1, 18, 1859, 20, 21, 2, 1]

50   [117, 10, 1, 12, 1, 14, 15, 32, 1, 18, 11, 20, 21, 338, 1]     15/11

51   [9, 10, 1859, 12, 1, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]     15/13

52   [9, 10, 11, 12, 1, 14, 15, 32, 1, 18, 169, 20, 21, 242, 1]

53   [9, 10, 11, 12, 1, 14, 15, 32, 1, 18, 371293, 20, 21, 242, 1]

54   [9, 10, 11, 12, 1, 14, 15, 32, 1, 18, 13, 20, 21, 242, 1]

55   [243, 10, 1859, 12, 1, 14, 15, 32, 1, 18, 1, 20, 21, 22, 1]

56   [243, 10, 11, 12, 1, 14, 15, 32, 1, 18, 169, 20, 21, 22, 1]

57   [243, 10, 11, 12, 1, 14, 15, 32, 1, 18, 371293, 20, 21, 22, 1]

58   [243, 10, 11, 12, 1, 14, 15, 32, 1, 18, 13, 20, 21, 22, 1]

59   [243, 10, 169, 12, 121, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

60   [243, 10, 371293, 12, 121, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

61   [243, 10, 13, 12, 121, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]     15/13

62   [243, 10, 1, 12, 1573, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]     15/11

63   [243, 10, 1, 12, 121, 14, 15, 32, 1, 18, 169, 20, 21, 2, 1]

64   [243, 10, 1, 12, 121, 14, 15, 32, 1, 18, 371293, 20, 21, 2, 1]

65   [243, 10, 1, 12, 121, 14, 15, 32, 1, 18, 13, 20, 21, 2, 1]

66   [243, 10, 169, 12, 161051, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

67   [243, 10, 371293, 12, 161051, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

68   [243, 10, 13, 12, 161051, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

69   [243, 10, 1, 12, 161051, 14, 15, 32, 1, 18, 169, 20, 21, 2, 1]

70   [243, 10, 1, 12, 161051, 14, 15, 32, 1, 18, 371293, 20, 21, 2, 1]

71   [243, 10, 1, 12, 161051, 14, 15, 32, 1, 18, 13, 20, 21, 2, 1]  15/11

72   [243, 10, 169, 12, 11, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]     15/13

73   [243, 10, 371293, 12, 11, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

74   [243, 10, 13, 12, 11, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]      15/13

75   [243, 10, 1, 12, 1859, 14, 15, 32, 1, 18, 1, 20, 21, 2, 1]

76   [243, 10, 1, 12, 11, 14, 15, 32, 1, 18, 169, 20, 21, 2, 1]

77   [243, 10, 1, 12, 11, 14, 15, 32, 1, 18, 371293, 20, 21, 2, 1]

78   [243, 10, 1, 12, 11, 14, 15, 32, 1, 18, 13, 20, 21, 2, 1]      15/11

79   [243, 10, 169, 12, 1, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]    15/13

80   [243, 10, 371293, 12, 1, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]

81   [243, 10, 13, 12, 1, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]     15/13

82   [243, 10, 1, 12, 169, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]    15/11

83   [243, 10, 1, 12, 371293, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]

84   [243, 10, 1, 12, 13, 14, 15, 32, 1, 18, 121, 20, 21, 2, 1]

85   [243, 10, 1, 12, 1, 14, 15, 32, 1, 18, 1573, 20, 21, 2, 1]

86   [243, 10, 169, 12, 1, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

87   [243, 10, 371293, 12, 1, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

88   [243, 10, 13, 12, 1, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

89   [243, 10, 1, 12, 169, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

90   [243, 10, 1, 12, 371293, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

91   [243, 10, 1, 12, 13, 14, 15, 32, 1, 18, 161051, 20, 21, 2, 1]

92   [243, 10, 169, 12, 1, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]

93   [243, 10, 371293, 12, 1, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]

94   [243, 10, 13, 12, 1, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]

95   [243, 10, 1, 12, 169, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]

96   [243, 10, 1, 12, 371293, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]

97   [243, 10, 1, 12, 13, 14, 15, 32, 1, 18, 11, 20, 21, 2, 1]

98   [243, 10, 1, 12, 1, 14, 15, 32, 1, 18, 1859, 20, 21, 2, 1]     15/11

99   [243, 10, 1859, 12, 1, 14, 15, 32, 1, 18, 1, 20, 21, 242, 1]   15/13

100   [243, 10, 11, 12, 1, 14, 15, 32, 1, 18, 169, 20, 21, 242, 1]

101   [243, 10, 11, 12, 1, 14, 15, 32, 1, 18, 371293, 20, 21, 242, 1]

102   [243, 10, 11, 12, 1, 14, 15, 32, 1, 18, 13, 20, 21, 242, 1]   15/13

[Dmitriy40]

Yadryara в сообщении #1575122 писал(а):

$94-64=30$. Покажите эту тридцатку, плиз.

Вот все 94:

(Оффтоп)

203 b62: 3^2.5 2.7^2 13^2 2^2.3 11^2 2.5^2 3 2^5 7 2.3^2 5 2^2 3 2 .
203 b66: 3^2.5 2.7^2 . 2^2.3 11^2 2.5^2 3.13^2 2^5 7 2.3^2 5 2^2 3 2 .
203 b67: 3^2.5 2.7^2 . 2^2.3 11^2 2.5^2 3 2^5 7.13^2 2.3^2 5 2^2 3 2 .
203 b68: 3^2.5 2.7^2 . 2^2.3 11^2 2.5^2 3 2^5 7 2.3^2 5.13^2 2^2 3 2 .
203 b70: 3^2.5 2.7^2 . 2^2.3 11^2 2.5^2 3 2^5 7 2.3^2 5 2^2 3.13^2 2 .
203 b88: 3^2.5 2.7^2 13^2 2^2.3 . 2.5^2 3.11^2 2^5 7 2.3^2 5 2^2 3 2 .
203 b91: 3^2.5 2.7^2 . 2^2.3 13^2 2.5^2 3.11^2 2^5 7 2.3^2 5 2^2 3 2 .
203 b94: 3^2.5 2.7^2 . 2^2.3 . 2.5^2 3.11^2 2^5 7.13^2 2.3^2 5 2^2 3 2 .
203 b95: 3^2.5 2.7^2 . 2^2.3 . 2.5^2 3.11^2 2^5 7 2.3^2 5.13^2 2^2 3 2 .
203 b97: 3^2.5 2.7^2 . 2^2.3 . 2.5^2 3.11^2 2^5 7 2.3^2 5 2^2 3.13^2 2 .
203 b98: 3^2.5 2.7^2 13^2 2^2.3 . 2.5^2 3 2^5 7.11^2 2.3^2 5 2^2 3 2 .
203 b101: 3^2.5 2.7^2 . 2^2.3 13^2 2.5^2 3 2^5 7.11^2 2.3^2 5 2^2 3 2 .
203 b104: 3^2.5 2.7^2 . 2^2.3 . 2.5^2 3.13^2 2^5 7.11^2 2.3^2 5 2^2 3 2 .
203 b105: 3^2.5 2.7^2 . 2^2.3 . 2.5^2 3 2^5 7.11^2 2.3^2 5.13^2 2^2 3 2 .
203 b107: 3^2.5 2.7^2 . 2^2.3 . 2.5^2 3 2^5 7.11^2 2.3^2 5 2^2 3.13^2 2 .
203 b108: 3^2.5 2.7^2 13^2 2^2.3 . 2.5^2 3 2^5 7 2.3^2 5.11^2 2^2 3 2 .
203 b111: 3^2.5 2.7^2 . 2^2.3 13^2 2.5^2 3 2^5 7 2.3^2 5.11^2 2^2 3 2 .
203 b114: 3^2.5 2.7^2 . 2^2.3 . 2.5^2 3.13^2 2^5 7 2.3^2 5.11^2 2^2 3 2 .
203 b115: 3^2.5 2.7^2 . 2^2.3 . 2.5^2 3 2^5 7.13^2 2.3^2 5.11^2 2^2 3 2 .
203 b117: 3^2.5 2.7^2 . 2^2.3 . 2.5^2 3 2^5 7 2.3^2 5.11^2 2^2 3.13^2 2 .
203 b118: 3^2.5 2.7^2 11.13^2 2^2.3 . 2.5^2 3 2^5 7 2.3^2 5 2^2 3 2.11^2 .
203 b119: 3^2.5 2.7^2 11 2^2.3 13^2 2.5^2 3 2^5 7 2.3^2 5 2^2 3 2.11^2 .
203 b122: 3^2.5 2.7^2 11 2^2.3 . 2.5^2 3.13^2 2^5 7 2.3^2 5 2^2 3 2.11^2 .
203 b123: 3^2.5 2.7^2 11 2^2.3 . 2.5^2 3 2^5 7.13^2 2.3^2 5 2^2 3 2.11^2 .
203 b124: 3^2.5 2.7^2 11 2^2.3 . 2.5^2 3 2^5 7 2.3^2 5.13^2 2^2 3 2.11^2 .
203 b126: 3^2.5 2.7^2 11 2^2.3 . 2.5^2 3 2^5 7 2.3^2 5 2^2 3.13^2 2.11^2 .
203 b141: 3^2.5 2.13^2 . 2^2.3 7^2 2.5^2 3.11^2 2^5 . 2.3^2 5 2^2.7 3 2 13
203 b142: 3^2.5 2 13^2 2^2.3 7^2 2.5^2 3.11^2 2^5 . 2.3^2 5 2^2.7 3 2 .
203 b146: 3^2.5 2 . 2^2.3 7^2 2.5^2 3.11^2 2^5 13^2 2.3^2 5 2^2.7 3 2 .
203 b149: 3^2.5 2 . 2^2.3 7^2 2.5^2 3.11^2 2^5 . 2.3^2 5.13^2 2^2.7 3 2 .
203 b150: 3^2.5 2 . 2^2.3 7^2 2.5^2 3.11^2 2^5 . 2.3^2 5 2^2.7 3.13^2 2 .
203 b151: 3^2.5 2.13^2 . 2^2.3 7^2 2.5^2 3 2^5 11^2 2.3^2 5 2^2.7 3 2 13
203 b152: 3^2.5 2 13^2 2^2.3 7^2 2.5^2 3 2^5 11^2 2.3^2 5 2^2.7 3 2 .
203 b156: 3^2.5 2 . 2^2.3 7^2 2.5^2 3.13^2 2^5 11^2 2.3^2 5 2^2.7 3 2 .
203 b158: 3^2.5 2 . 2^2.3 7^2 2.5^2 3 2^5 11^2 2.3^2 5.13^2 2^2.7 3 2 .
203 b159: 3^2.5 2 . 2^2.3 7^2 2.5^2 3 2^5 11^2 2.3^2 5 2^2.7 3.13^2 2 .
203 b177: 3^2.5 2.13^2 . 2^2.3 7^2 2.5^2 3 2^5 . 2.3^2 5.11^2 2^2.7 3 2 13
203 b178: 3^2.5 2 13^2 2^2.3 7^2 2.5^2 3 2^5 . 2.3^2 5.11^2 2^2.7 3 2 .
203 b182: 3^2.5 2 . 2^2.3 7^2 2.5^2 3.13^2 2^5 . 2.3^2 5.11^2 2^2.7 3 2 .
203 b183: 3^2.5 2 . 2^2.3 7^2 2.5^2 3 2^5 13^2 2.3^2 5.11^2 2^2.7 3 2 .
203 b186: 3^2.5 2 . 2^2.3 7^2 2.5^2 3 2^5 . 2.3^2 5.11^2 2^2.7 3.13^2 2 .
203 b187: 3^2.5 2.13^2 11 2^2.3 7^2 2.5^2 3 2^5 . 2.3^2 5 2^2.7 3 2.11^2 13
203 b188: 3^2.5 2 11.13^2 2^2.3 7^2 2.5^2 3 2^5 . 2.3^2 5 2^2.7 3 2.11^2 .
203 b190: 3^2.5 2 11 2^2.3 7^2 2.5^2 3.13^2 2^5 . 2.3^2 5 2^2.7 3 2.11^2 .
203 b191: 3^2.5 2 11 2^2.3 7^2 2.5^2 3 2^5 13^2 2.3^2 5 2^2.7 3 2.11^2 .
203 b194: 3^2.5 2 11 2^2.3 7^2 2.5^2 3 2^5 . 2.3^2 5.13^2 2^2.7 3 2.11^2 .
203 b195: 3^2.5 2 11 2^2.3 7^2 2.5^2 3 2^5 . 2.3^2 5 2^2.7 3.13^2 2.11^2 .
203 b438: . 2.11^2 3.13^2 2^2.7 5 2.3^2 . 2^5 3 2.5^2 7^2 2^2.3 11 2 3^2.5
203 b439: . 2.11^2 3 2^2.7 5.13^2 2.3^2 . 2^5 3 2.5^2 7^2 2^2.3 11 2 3^2.5
203 b440: . 2.11^2 3 2^2.7 5 2.3^2 13^2 2^5 3 2.5^2 7^2 2^2.3 11 2 3^2.5
203 b443: . 2.11^2 3 2^2.7 5 2.3^2 . 2^5 3.13^2 2.5^2 7^2 2^2.3 11 2 3^2.5
203 b445: . 2.11^2 3 2^2.7 5 2.3^2 . 2^5 3 2.5^2 7^2 2^2.3 11.13^2 2 3^2.5
203 b446: 13 2.11^2 3 2^2.7 5 2.3^2 . 2^5 3 2.5^2 7^2 2^2.3 11 2.13^2 3^2.5
203 b447: . 2 3.13^2 2^2.7 5.11^2 2.3^2 . 2^5 3 2.5^2 7^2 2^2.3 . 2 3^2.5
203 b448: . 2 3 2^2.7 5.11^2 2.3^2 13^2 2^5 3 2.5^2 7^2 2^2.3 . 2 3^2.5
203 b451: . 2 3 2^2.7 5.11^2 2.3^2 . 2^5 3.13^2 2.5^2 7^2 2^2.3 . 2 3^2.5
203 b453: . 2 3 2^2.7 5.11^2 2.3^2 . 2^5 3 2.5^2 7^2 2^2.3 13^2 2 3^2.5
203 b456: 13 2 3 2^2.7 5.11^2 2.3^2 . 2^5 3 2.5^2 7^2 2^2.3 . 2.13^2 3^2.5
203 b457: . 2 3.13^2 2^2.7 5 2.3^2 11^2 2^5 3 2.5^2 7^2 2^2.3 . 2 3^2.5
203 b458: . 2 3 2^2.7 5.13^2 2.3^2 11^2 2^5 3 2.5^2 7^2 2^2.3 . 2 3^2.5
203 b460: . 2 3 2^2.7 5 2.3^2 11^2 2^5 3.13^2 2.5^2 7^2 2^2.3 . 2 3^2.5
203 b462: . 2 3 2^2.7 5 2.3^2 11^2 2^5 3 2.5^2 7^2 2^2.3 13^2 2 3^2.5
203 b465: 13 2 3 2^2.7 5 2.3^2 11^2 2^5 3 2.5^2 7^2 2^2.3 . 2.13^2 3^2.5
203 b483: . 2 3.13^2 2^2.7 5 2.3^2 . 2^5 3.11^2 2.5^2 7^2 2^2.3 . 2 3^2.5
203 b484: . 2 3 2^2.7 5.13^2 2.3^2 . 2^5 3.11^2 2.5^2 7^2 2^2.3 . 2 3^2.5
203 b485: . 2 3 2^2.7 5 2.3^2 13^2 2^5 3.11^2 2.5^2 7^2 2^2.3 . 2 3^2.5
203 b489: . 2 3 2^2.7 5 2.3^2 . 2^5 3.11^2 2.5^2 7^2 2^2.3 13^2 2 3^2.5
203 b492: 13 2 3 2^2.7 5 2.3^2 . 2^5 3.11^2 2.5^2 7^2 2^2.3 . 2.13^2 3^2.5
203 b552: . 2.11^2 3.13^2 2^2 5 2.3^2 7 2^5 3 2.5^2 . 2^2.3 11 2.7^2 3^2.5
203 b554: . 2.11^2 3 2^2 5.13^2 2.3^2 7 2^5 3 2.5^2 . 2^2.3 11 2.7^2 3^2.5
203 b555: . 2.11^2 3 2^2 5 2.3^2 7.13^2 2^5 3 2.5^2 . 2^2.3 11 2.7^2 3^2.5
203 b556: . 2.11^2 3 2^2 5 2.3^2 7 2^5 3.13^2 2.5^2 . 2^2.3 11 2.7^2 3^2.5
203 b557: . 2.11^2 3 2^2 5 2.3^2 7 2^5 3 2.5^2 13^2 2^2.3 11 2.7^2 3^2.5
203 b560: . 2.11^2 3 2^2 5 2.3^2 7 2^5 3 2.5^2 . 2^2.3 11.13^2 2.7^2 3^2.5
203 b561: . 2 3.13^2 2^2 5.11^2 2.3^2 7 2^5 3 2.5^2 . 2^2.3 . 2.7^2 3^2.5
203 b563: . 2 3 2^2 5.11^2 2.3^2 7.13^2 2^5 3 2.5^2 . 2^2.3 . 2.7^2 3^2.5
203 b564: . 2 3 2^2 5.11^2 2.3^2 7 2^5 3.13^2 2.5^2 . 2^2.3 . 2.7^2 3^2.5
203 b565: . 2 3 2^2 5.11^2 2.3^2 7 2^5 3 2.5^2 13^2 2^2.3 . 2.7^2 3^2.5
203 b568: . 2 3 2^2 5.11^2 2.3^2 7 2^5 3 2.5^2 . 2^2.3 13^2 2.7^2 3^2.5
203 b572: . 2 3.13^2 2^2 5 2.3^2 7.11^2 2^5 3 2.5^2 . 2^2.3 . 2.7^2 3^2.5
203 b574: . 2 3 2^2 5.13^2 2.3^2 7.11^2 2^5 3 2.5^2 . 2^2.3 . 2.7^2 3^2.5
203 b575: . 2 3 2^2 5 2.3^2 7.11^2 2^5 3.13^2 2.5^2 . 2^2.3 . 2.7^2 3^2.5
203 b576: . 2 3 2^2 5 2.3^2 7.11^2 2^5 3 2.5^2 13^2 2^2.3 . 2.7^2 3^2.5
203 b579: . 2 3 2^2 5 2.3^2 7.11^2 2^5 3 2.5^2 . 2^2.3 13^2 2.7^2 3^2.5
203 b583: . 2 3.13^2 2^2 5 2.3^2 7 2^5 3.11^2 2.5^2 . 2^2.3 . 2.7^2 3^2.5
203 b585: . 2 3 2^2 5.13^2 2.3^2 7 2^5 3.11^2 2.5^2 . 2^2.3 . 2.7^2 3^2.5
203 b586: . 2 3 2^2 5 2.3^2 7.13^2 2^5 3.11^2 2.5^2 . 2^2.3 . 2.7^2 3^2.5
203 b587: . 2 3 2^2 5 2.3^2 7 2^5 3.11^2 2.5^2 13^2 2^2.3 . 2.7^2 3^2.5
203 b590: . 2 3 2^2 5 2.3^2 7 2^5 3.11^2 2.5^2 . 2^2.3 13^2 2.7^2 3^2.5
203 b593: . 2 3.13^2 2^2 5 2.3^2 7 2^5 3 2.5^2 11^2 2^2.3 . 2.7^2 3^2.5
203 b595: . 2 3 2^2 5.13^2 2.3^2 7 2^5 3 2.5^2 11^2 2^2.3 . 2.7^2 3^2.5
203 b596: . 2 3 2^2 5 2.3^2 7.13^2 2^5 3 2.5^2 11^2 2^2.3 . 2.7^2 3^2.5
203 b597: . 2 3 2^2 5 2.3^2 7 2^5 3.13^2 2.5^2 11^2 2^2.3 . 2.7^2 3^2.5
203 b599: . 2 3 2^2 5 2.3^2 7 2^5 3 2.5^2 11^2 2^2.3 13^2 2.7^2 3^2.5

[Yadryara]

Dmitriy40 в сообщении #1575164 писал(а):

203 b118: 3^2.5 2.7^2 11.13^2 2^2.3 . 2.5^2 3 2^5 7 2.3^2 5 2^2 3 2.11^2 .
203 b119: 3^2.5 2.7^2 11 2^2.3 13^2 2.5^2 3 2^5 7 2.3^2 5 2^2 3 2.11^2 .

Ну а что делают здесь, например, эти 2 варианта? В них ведь 12 CP, а не 11 !

В первом случае один чистый квадрат(2^2) и две точки.

Во втором случае два чистых квадрата(2^2 и 13^2) и одна точка.

То есть по 3 куаровских места. Значит $15-3=12$ CP.

Видимо в этом списке как раз 30 таких вариантов, где не 11 CP.

[Dmitriy40]

Yadryara
Сделаем по другому: вот программа pats2.gp для подсчёта количества CP (вообще не понимаю зачем Вы считаете и простые в квадрате, но пусть):

Hugo=readstr("D12n15-all.pats");\\Список всех 1251 паттернов Hugo
{for(i=1,#Hugo,
   s=strsplit(Hugo[i]," "); if(s[1]!="203", next); n=0;\\Обрабатываем только список паттернов
   for(t=1,15,
      if(s[t+2]==".", h=1, h=eval(strjoin(strsplit(s[t+2],"."),"*")));
      if(h==8 || h==6, next(2));\\Такие паттерны запрещены и считать не будем
      x=numdiv(h); if(x==2||x==6||x==4, n++);\\Считаем и p и p^2
   );
   print(Hugo[i]," [check=",n,"]");
)}
quit;

Вот статистика после её запуска:

T:\M12minimal\Hugo>gp32 -q pats2.gp >pats2.gp.D12n15

T:\M12minimal\Hugo>for /l %n in (7,1,15) do @echo check=%n:&&find /c "check=%n" pats2.gp.D12n15
check=7:
---------- PATS2.GP.D12N15: 0
check=8:
---------- PATS2.GP.D12N15: 0
check=9:
---------- PATS2.GP.D12N15: 4
check=10:
---------- PATS2.GP.D12N15: 32
check=11:
---------- PATS2.GP.D12N15: 120
check=12:
---------- PATS2.GP.D12N15: 243
check=13:
---------- PATS2.GP.D12N15: 193
check=14:
---------- PATS2.GP.D12N15: 38
check=15:
---------- PATS2.GP.D12N15: 0

T:\M12minimal\Hugo>findstr "check=9" pats2.gp.D12n15
203 b8: 3^2 2.5 13^2 2^2.3 11^2 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2 . [sq=4] [check=9]
203 b12: 3^2 2.5 . 2^2.3 11^2 2.7 3.5 2^5 . 2.3^2 13^2 2^2.5 3.7 2 . [sq=4] [check=9]
203 b31: 3^2 2.5 13^2 2^2.3 . 2.7 3.5 2^5 . 2.3^2 11^2 2^2.5 3.7 2 . [sq=4] [check=9]
203 b34: 3^2 2.5 . 2^2.3 13^2 2.7 3.5 2^5 . 2.3^2 11^2 2^2.5 3.7 2 . [sq=4] [check=9]

T:\M12minimal\Hugo>findstr "check=10" pats2.gp.D12n15
203 b0: 3^2 2.5 11.13^2 2^2.3 . 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2.11 . [sq=5] [check=10]
203 b1: 3^2 2.5 11 2^2.3 13^2 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2.11 . [sq=5] [check=10]
203 b5: 3^2 2.5 11 2^2.3 . 2.7 3.5 2^5 . 2.3^2 13^2 2^2.5 3.7 2.11 . [sq=5] [check=10]
203 b9: 3^2 2.5 13^5 2^2.3 11^2 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2 . [sq=4] [check=10]
203 b10: 3^2 2.5 13 2^2.3 11^2 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2 . [sq=4] [check=10]
203 b11: 3^2 2.5 . 2^2.3 11^2.13 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2 . [sq=4] [check=10]
203 b13: 3^2 2.5 . 2^2.3 11^2 2.7 3.5 2^5 . 2.3^2 13^5 2^2.5 3.7 2 . [sq=4] [check=10]
203 b14: 3^2 2.5 . 2^2.3 11^2 2.7 3.5 2^5 . 2.3^2 13 2^2.5 3.7 2 . [sq=4] [check=10]
203 b15: 3^2.13 2.5 . 2^2.3 11^2 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2.13^2 . [sq=4] [check=10]
203 b16: 3^2 2.5 13^2 2^2.3 11^5 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2 . [sq=4] [check=10]
203 b19: 3^2 2.5 . 2^2.3 11^5 2.7 3.5 2^5 . 2.3^2 13^2 2^2.5 3.7 2 . [sq=4] [check=10]
203 b23: 3^2 2.5 13^2 2^2.3 11 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2 . [sq=4] [check=10]
203 b26: 3^2 2.5 . 2^2.3 11.13^2 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2 . [sq=4] [check=10]
203 b27: 3^2 2.5 . 2^2.3 11 2.7 3.5 2^5 . 2.3^2 13^2 2^2.5 3.7 2 . [sq=4] [check=10]
203 b32: 3^2 2.5 13^5 2^2.3 . 2.7 3.5 2^5 . 2.3^2 11^2 2^2.5 3.7 2 . [sq=4] [check=10]
203 b33: 3^2 2.5 13 2^2.3 . 2.7 3.5 2^5 . 2.3^2 11^2 2^2.5 3.7 2 . [sq=4] [check=10]
203 b35: 3^2 2.5 . 2^2.3 13^5 2.7 3.5 2^5 . 2.3^2 11^2 2^2.5 3.7 2 . [sq=4] [check=10]
203 b36: 3^2 2.5 . 2^2.3 13 2.7 3.5 2^5 . 2.3^2 11^2 2^2.5 3.7 2 . [sq=4] [check=10]
203 b37: 3^2 2.5 . 2^2.3 . 2.7 3.5 2^5 . 2.3^2 11^2.13 2^2.5 3.7 2 . [sq=4] [check=10]
203 b38: 3^2.13 2.5 . 2^2.3 . 2.7 3.5 2^5 . 2.3^2 11^2 2^2.5 3.7 2.13^2 . [sq=4] [check=10]
203 b39: 3^2 2.5 13^2 2^2.3 . 2.7 3.5 2^5 . 2.3^2 11^5 2^2.5 3.7 2 . [sq=4] [check=10]
203 b42: 3^2 2.5 . 2^2.3 13^2 2.7 3.5 2^5 . 2.3^2 11^5 2^2.5 3.7 2 . [sq=4] [check=10]
203 b46: 3^2 2.5 13^2 2^2.3 . 2.7 3.5 2^5 . 2.3^2 11 2^2.5 3.7 2 . [sq=4] [check=10]
203 b49: 3^2 2.5 . 2^2.3 13^2 2.7 3.5 2^5 . 2.3^2 11 2^2.5 3.7 2 . [sq=4] [check=10]
203 b52: 3^2 2.5 . 2^2.3 . 2.7 3.5 2^5 . 2.3^2 11.13^2 2^2.5 3.7 2 . [sq=4] [check=10]
203 b54: 3^2 2.5 11.13^2 2^2.3 . 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2.11^2 . [sq=4] [check=10]
203 b55: 3^2 2.5 11 2^2.3 13^2 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2.11^2 . [sq=4] [check=10]
203 b59: 3^2 2.5 11 2^2.3 . 2.7 3.5 2^5 . 2.3^2 13^2 2^2.5 3.7 2.11^2 . [sq=4] [check=10]
203 b325: 3^5 2.5 13^2 2^2.3 11^2 2.7 3.5 2^5 . 2.3^2 . 2^2.5 3.7 2 . [sq=4] [check=10]
203 b329: 3^5 2.5 . 2^2.3 11^2 2.7 3.5 2^5 . 2.3^2 13^2 2^2.5 3.7 2 . [sq=4] [check=10]
203 b345: 3^5 2.5 13^2 2^2.3 . 2.7 3.5 2^5 . 2.3^2 11^2 2^2.5 3.7 2 . [sq=4] [check=10]
203 b348: 3^5 2.5 . 2^2.3 13^2 2.7 3.5 2^5 . 2.3^2 11^2 2^2.5 3.7 2 . [sq=4] [check=10]

T:\M12minimal\Hugo>for /l %n in (11,1,14) do @echo check=%n:&&findstr /V "sq" pats2.gp.D12n15|find /c "check=%n"
check=11:
64
check=12:
208
check=13:
180
check=14:
36

Как-то оно не совсем совпадает с Вашими данными.

[Yadryara]

Dmitriy40 в сообщении #1575179 писал(а):

Как-то оно не совсем совпадает с Вашими данными.

В одном списке у Вас в сумме 630 паттернов. У меня 528, потому что я 102 отбросил(показал какие именно отбросил и почему).$630-102=528$.

В другом списке у Вас в сумме 488 паттернов. У меня столько же основных, как уже писал. $488+40=528$.

Сравниваем эти списки.

Ваш:

Dmitriy40 в сообщении #1575179 писал(а):

check=11: 64
check=12: 208
check=13: 180
check=14: 36

Мой:

Yadryara в сообщении #1575113 писал(а):

CP    Patterns

10           2
11          72
12         223
13         193
14          36
15           0
______________
           528

Теперь смотрим на мою таблицу с разделением. Основные слева.

CP         Patterns

10           0 +  2
11          64 +  8
12         208 + 15
13         180 + 13
14          36 +  2
___________________
           488 + 40 = 528

Что-то не сходится ?

[Yadryara]

А каково максимальное количество квадратов простых(Max-p^2), которые можно расставить в эти 528 паттернов для 15-шек ?

Max-p^2   Patterns

4               12
5                4
6              228
7              232
8               50
9                2
__________________
               528

Паттерн, в котором уже расставлены все квадраты простых, назову неделимым.

Постепенно приближаюсь к ответу на вопрос: а сколько же неделимых паттернов нужно обсчитать, чтобы полностью проверить весь диапазон до нынешней минимальной 15-шки ?

[Dmitriy40]

Yadryara в сообщении #1575199 писал(а):

Что-то не сходится ?

Да: не вижу цифры 120 для CP=11, цифры 32 для CP=10, цифры 4 для CP=9.

Yadryara в сообщении #1575202 писал(а):

А каково максимальное количество квадратов простых(Max-p^2), которые можно расставить в эти 528 паттернов для 15-шек ?

И это тоже не сходится:

T:\M12minimal\Hugo>for /l %n in (1,1,15) do @echo %n:&&find /c "[primes=%n]" pats2.gp.D12n15
1:---------- PATS2.GP.D12N15: 0
2:---------- PATS2.GP.D12N15: 0
3:---------- PATS2.GP.D12N15: 0
4:---------- PATS2.GP.D12N15: 0
5:---------- PATS2.GP.D12N15: 0
6:---------- PATS2.GP.D12N15: 212
7:---------- PATS2.GP.D12N15: 239
8:---------- PATS2.GP.D12N15: 105
9:---------- PATS2.GP.D12N15: 60
10:--------- PATS2.GP.D12N15: 14
11:--------- PATS2.GP.D12N15: 0
12:--------- PATS2.GP.D12N15: 0
13:--------- PATS2.GP.D12N15: 0
14:--------- PATS2.GP.D12N15: 0
15:--------- PATS2.GP.D12N15: 0