Other Primes
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Today mathematics, unlike the old like Muncey, don't consider a prime magic square a square containing the prime number 1 with other primes. Else, in the previous generated square I consider (like Muncey) that the prime 2 was substituted by prime 1, so the this was a sequence of "consecutive" primes: 1, 3, 5, 7, ...
This is not true, but now I have the automatic program that go very fast, so if I use really sequence of prime I can do the study like in previous work. In the next, I use call a xx sequence square, the prime magic square builded used a sequence of consecutive primes starting from prime xx.
The below tables are builded like in the same case (that I have report another time, to show you how I look for): calculate the magic constant for that order and build a square of that order to say if the square exists.

Sequence From Number 1 | Max Order 449
Order Magic Constant Esistence
1 1 YES
2 8 NO
3 33 NO
4 95 NO
12 4514 YES (with double)
15 9635 YES
17 14691 YES
22 34926 YES
30 97849 NO
35 162759 YES
78 2224007 NO
98 4648955 NO
124 9912840 YES
191 39541261 ?

Sequence From Prime 3 | Max Order 275
Order Magic Constant Esistence
1 3 YES
2 13 NO
12 4583 NO
35 163043 ?
215 57689237 ?
225 66684561 ?

Sequence From Prime 5 | Max Order 270
Order Magic Constant Esistence
1 5 YES
2 18 NO
4 124 ?
6 457 NO
30 98316 ?
33 134641 ?
37 195975 ?
45 372165 ?
95 4207781 ?
151 18651841 ?
204 48795474 ?

Sequence From Prime 7 | Max Order 314
Order Magic Constant Esistence
1 7 YES
2 24 NO
6 484 YES
7 797 YES
10 2579 NO
254 98119026 ?

Sequence From Prime 11 | Max Order 314
Order Magic Constant Esistence
1 11 YES
2 30 NO
52 597531 NO
130 11544010 ?
190 38892849 NO
232 73532440 ?

Sequence From Prime 13 | Max Order 276
Order Magic Constant Esistence
1 13 YES
2 36 NO
4 161 NO
5 313 YES
13 6325 YES
28 78960 YES
191 39552623 ?
213 56005545 ?

Sequence From Prime 17 | Max Order 238
Order Magic Constant Esistence
1 17 YES
2 44 NO
56 761542 ?
138 13983894 ?
178 31578328 ?

Sequence From Prime 19 | Max Order 249
Order Magic Constant Esistence
1 19 YES
2 51 NO
4 204 ?
36 180596 ?
41 276243 ?
42 298868 ?
92 3798666 ?
146 16752939 NO
187 36971337 ?

Sequence From Prime 23 | Max Order 259
Order Magic Constant Esistence
1 23 YES
2 60 NO
3 121 NO
10 2862 YES
16 12807 NO
18 18789 NO
28 79608 YES
31 111023 ?
62 1061019 NO
131 11837081 ?

Sequence From Prime 29 | Max Order 233
Order Magic Constant Esistence
1 29 YES
2 69 NO
4 240 ?
40 255529 NO
47 431917 ?

Sequence From Prime 31 | Max Order 234
Order Magic Constant Esistence
1 31 YES
2 76 NO
4 258 YES
6 683 NO
16 13016 YES
36 181486 ?
129 11269985 ?
222 63917480 ?

Sequence From Prime 37 | Max Order 235
Order Magic Constant Esistence
1 37 YES
2 84 NO
4 276 YES
6 713 NO
7 1077 YES
9 2211 YES
24 48601 NO
30 100429 NO
31 111761 ?
33 137035 ?
36 181783 NO
55 720739 ?
118 8467046 ?
150 18274476 ?
152 19066090 ?

Sequence From Prime 41 | Max Order 254
Order Magic Constant Esistence
1 41 YES
2 92 NO
6 744 YES
8 1613 NO
9 2261 YES
10 3092 YES
23 42515 NO
36 182080 ?
54 679584 ?
144 16036654 ?

Sequence From Prime 43 | Max Order 279
Order Magic Constant Esistence
1 43 YES
2 101 NO
6 775 NO
9 2311 YES
14 8763 NO
19 23069 YES
32 124454 ?
36 182377 NO
61 1009425 ?
92 3804356 ?
118 8469605 NO
132 12136595 NO
149 17890747 ?
150 18277887 NO

Sequence From Prime 47 | Max Order 248
Order Magic Constant Esistence
1 47 YES
2 110 NO
4 328 ?
6 806 YES
18 19530 YES
53 640571 ?

Sequence From Prime 53 | Max Order 270
Order Magic Constant Esistence
1 53 YES
2 120 NO
4 348 ?
6 837 NO
8 1745 NO
13 7125 ?
26 63839 NO
91 3674603 ?
147 17136689 ?
180 32745429 NO
238 79796540 ?

Sequence From Prime 59 | Max Order 245
Order Magic Constant Esistence
1 59 YES
2 129 NO
5 577 YES
6 868 YES
9 2463 YES
24 49489 NO
38 218432 ?
39 237623 ?
148 17514360 ?

Sequence From Prime 61 | Max Order 110
Order Magic Constant Esistence
1 61 YES
2 136 NO
4 387 NO
101 5141345 ?

Sequence From Prime 67 | Max Order 110
Order Magic Constant Esistence
1 67 YES
2 145 NO
6 930 YES
11 4507 YES
24 49846 YES
30 102086 ?
34 152952 ?
41 280109 ?

Sequence From Prime 71 | Max Order 110
Order Magic Constant Esistence
1 71 YES
2 153 NO
4 427 NO
8 1925 NO
10 3500 YES
13 7449 ?
17 16857 YES
33 139171 ?
35 168199 ?
40 258933 NO
69 1507575 ?

Sequence From Prime 73 | Max Order 100
Order Magic Constant Esistence
1 73 YES
2 162 NO
4 447 NO
20 28184 YES
67 1371759 ?

Sequence From Prime 79 | Max Order 100
Order Magic Constant Esistence
1 79 YES
2 174 NO
4 468 ?
5 703 YES
8 2016 YES
9 2725 YES
12 6037 NO
27 73385 YES
41 281167 ?
56 769283 NO
78 2240267 NO
86 3068335 NO
90 3551722 ?

Sequence From Prime 83 | Max Order 252
Order Magic Constant Esistence
1 83 YES
2 185 NO
4 489 NO
10 3677 NO

Sequence From Prime 89 | Max Order 170
Order Magic Constant Esistence
1 89 YES
2 195 NO
4 510 ?
11 4845 ?
12 6188 YES
14 9660 YES
30 103275 NO
48 468555 NO
58 862750 ?
144 16054533 NO

 
 
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