Покажу три пандиагональных квадрата 16-го порядка из различных простых чисел,
иллюстрирующих три метода построения.
№1
Код:
19 67 83 109 * Potential scam. Censored * * Potential scam. Censored * * Potential scam. Censored *
* Potential scam. Censored * * Potential scam. Censored * * Potential scam. Censored * 2843 2549 1597
* Potential scam. Censored * * Potential scam. Censored * * Potential scam. Censored * 2753 2129 1933
* Potential scam. Censored * * Potential scam. Censored * * Potential scam. Censored * 2003 2633 2393
* Potential scam. Censored * * Potential scam. Censored * 1069 337 593 569 * Potential scam. Censored *
* Potential scam. Censored * * Potential scam. Censored * 487 1459 1039 353 * Potential scam. Censored *
* Potential scam. Censored * * Potential scam. Censored * * Potential scam. Censored * 5647 5527 4973
* Potential scam. Censored * * Potential scam. Censored * 503 997 733 * Potential scam. Censored * 4729
* Potential scam. Censored * * Potential scam. Censored * * Potential scam. Censored * 53 79 103 127
* Potential scam. Censored * * Potential scam. Censored * * Potential scam. Censored * 149 163 167 193
* Potential scam. Censored * * Potential scam. Censored * * Potential scam. Censored * 263 269 257 383
* Potential scam. Censored * * Potential scam. Censored * * Potential scam. Censored * 443 659 563 797
* Potential scam. Censored * 1103 349 613 587 * Potential scam. Censored * * Potential scam. Censored *
* Potential scam. Censored * 499 1483 1049 367 * Potential scam. Censored * * Potential scam. Censored *
* Potential scam. Censored * 683 359 479 * Potential scam. Censored * * Potential scam. Censored * 4723
* Potential scam. Censored * 599 1223 773 * Potential scam. Censored * * Potential scam. Censored * 4093

Этот квадрат построен с помощью решёток Россера из 16 пандиагональных квадратов 4-го порядка.
(см.
http://www.natalimak1.narod.ru/kompl556.htm )
№2
Код:
1087 619 2089 607 1249 677 397 * Potential scam. Censored * 2053 151 1543 2213 2857
1481 1063 421 2801 271 2843 773 1549 857 * Potential scam. Censored * 1013 313 2027
179 1997 3121 2099 683 3019 1483 2221 443 * Potential scam. Censored * 223 601 907
2953 3089 2551 863 2557 1597 181 1367 2777 461 113 1723 1823 109 1409 1627
* Potential scam. Censored * 1721 101 2477 479 2683 2609 839 1019 233 2081 2719 769
193 3119 127 1913 2297 1873 751 139 * Potential scam. Censored * 3083 881 971 709
* Potential scam. Censored * 2803 947 * Potential scam. Censored * 811 2887 3137 241 1789
761 2693 2239 463 * Potential scam. Censored * 41 1619 2341 83 733 3079 1171 1303
1949 353 149 1097 2999 1607 937 293 * Potential scam. Censored * 1901 2473 2753 491
2293 1453 383 419 557 * Potential scam. Censored * 2087 2729 349 2879 307 2377 1601
2707 1987 401 1579 409 * Potential scam. Censored * 1153 29 1051 2467 131 1667 929
373 * Potential scam. Censored * 3041 * Potential scam. Censored * 2287 593 1553 2969 1783
467 541 * Potential scam. Censored * 431 2381 883 * Potential scam. Censored * 3049 673 2671
* Potential scam. Censored * * Potential scam. Censored * 31 3023 1237 853 1277 2399 3011
2459 * Potential scam. Censored * 2909 1361 439 1867 1861 1567 347 2203 2153 1999
3109 1531 809 3067 2417 71 1979 1847 2389 457 911 2687 487 2141 571 727

Этот квадрат получен с помощью преобразования 3-х квадрантов из ассоциативного квадрата, построенного методом точных ортогональных покрытий.
(см.
post989356.html#p989356 )
№3 (автор
Jarek)
Код:
(7,109,467,829,1423,349,1607,1129,197,701,1483,401,827,1997,613,1301), (127,809,1567,419,547,509,37,1409,1823,2011,503,31,743,691,1277,937), (1847,1031,1453,1361,1487,641,523,491,1153,1039,137,1699,73,79,47,379), (53,1531,263,211,773,1741,1103,241,277,569,1297,89,1867,1049,1087,1289), (643,1579,677,1609,283,1459,1097,859,617,11,1033,881,1637,191,733,131), (1747,1229,577,479,1237,359,877,719,563,601,293,1231,1193,151,233,1951), (1217,101,163,41,317,761,433,281,1123,769,947,2029,1543,1249,977,1489), (683,811,983,541,1493,661,863,1381,157,1499,607,1319,1447,269,487,239), (1663,739,857,1669,853,139,1307,499,647,1511,43,431,887,911,463,821), (97,179,1657,2069,457,839,997,449,1523,991,383,751,23,1171,1583,271), (17,311,1093,521,1427,1871,1303,1601,1723,1069,557,19,373,619,227,709), (443,331,173,1801,113,61,1223,1051,967,29,2287,1619,787,389,727,1439), (883,1759,797,229,823,439,257,919,587,71,223,251,1367,1571,1783,1481), (2557,1259,907,1019,367,929,337,149,83,421,953,1021,353,1291,1163,631), (347,1091,1213,461,107,1061,193,941,673,1549,2297,1009,13,199,1973,313), (1109,571,593,181,1733,1621,1283,1321,1327,599,397,659,307,1613,67,59)

(см.
http://trdb.org/Contest/PandiagonalMagi ... inalReport )
Совершенствуются алгоритмы – улучшаются результаты.
И это, скорее всего, ещё не минимальное решение. Согласно последовательности OEIS
A164843 нижняя граница магической константы пандиагонального квадрата 16-го порядка из различных простых чисел равна
12088.