Other Primes

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.

 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 ?

 Order Magic Constant Esistence 1 3 YES 2 13 NO 12 4583 NO 35 163043 ? 215 57689237 ? 225 66684561 ?

 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 ?

 Order Magic Constant Esistence 1 7 YES 2 24 NO 6 484 YES 7 797 YES 10 2579 NO 254 98119026 ?

 Order Magic Constant Esistence 1 11 YES 2 30 NO 52 597531 NO 130 11544010 ? 190 38892849 NO 232 73532440 ?

 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 ?

 Order Magic Constant Esistence 1 17 YES 2 44 NO 56 761542 ? 138 13983894 ? 178 31578328 ?

 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 ?

 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 ?

 Order Magic Constant Esistence 1 29 YES 2 69 NO 4 240 ? 40 255529 NO 47 431917 ?

 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 ?

 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 ?

 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 ?

 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

 Order Magic Constant Esistence 1 47 YES 2 110 NO 4 328 ? 6 806 YES 18 19530 YES 53 640571 ?

 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 ?

 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 ?

 Order Magic Constant Esistence 1 61 YES 2 136 NO 4 387 NO 101 5141345 ?

 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 ?

 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 ?

 Order Magic Constant Esistence 1 73 YES 2 162 NO 4 447 NO 20 28184 YES 67 1371759 ?

 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 ?

 Order Magic Constant Esistence 1 83 YES 2 185 NO 4 489 NO 10 3677 NO

 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

 Magic Square Tognon Stefano Research