so, jetzt hab ich noch ein paar zahlen gefunden, für die x^2+y^2=p gilt, wobei p eine primzahl ist:
x = 1, y = 1, p = 2
x = 1, y = 4, p = 5
x = 1, y = 16, p = 17
x = 1, y = 36, p = 37
x = 1, y = 196, p = 197
x = 1, y = 256, p = 257
x = 1, y = 576, p = 577
x = 1, y = 1296, p = 1297
x = 4, y = 1, p = 5
x = 4, y = 9, p = 13
x = 4, y = 49, p = 53
x = 4, y = 100, p = 104
x = 4, y = 289, p = 293
x = 4, y = 484, p = 488
x = 4, y = 729, p = 733
x = 4, y = 784, p = 788
x = 4, y = 1089, p = 1093
x = 4, y = 1225, p = 1229
x = 4, y = 1369, p = 1373
x = 9, y = 4, p = 13
x = 9, y = 64, p = 73
x = 9, y = 225, p = 234
x = 9, y = 441, p = 450
x = 9, y = 1024, p = 1033
x = 9, y = 1444, p = 1453
x = 16, y = 1, p = 17
x = 16, y = 25, p = 41
x = 16, y = 81, p = 97
x = 16, y = 121, p = 137
x = 16, y = 484, p = 500
x = 16, y = 676, p = 692
x = 25, y = 4, p = 29
x = 25, y = 16, p = 41
x = 25, y = 36, p = 61
x = 25, y = 64, p = 89
x = 25, y = 169, p = 194
x = 25, y = 256, p = 281
x = 25, y = 324, p = 349
x = 25, y = 576, p = 601
x = 25, y = 1024, p = 1049
x = 25, y = 1156, p = 1181
x = 25, y = 1296, p = 1321
x = 36, y = 1, p = 37
x = 36, y = 25, p = 61
x = 36, y = 121, p = 157
x = 36, y = 361, p = 397
x = 49, y = 4, p = 53
x = 49, y = 64, p = 113
x = 49, y = 100, p = 149
x = 49, y = 144, p = 193
x = 49, y = 324, p = 373
x = 49, y = 529, p = 578
x = 49, y = 625, p = 674
x = 49, y = 961, p = 1010
x = 49, y = 1444, p = 1493
x = 64, y = 9, p = 73
x = 64, y = 25, p = 89
x = 64, y = 49, p = 113
x = 64, y = 289, p = 353
x = 64, y = 400, p = 464
x = 64, y = 676, p = 740
x = 64, y = 1089, p = 1153
x = 64, y = 1225, p = 1289
x = 64, y = 1369, p = 1433
x = 64, y = 1600, p = 1664
x = 81, y = 16, p = 97
x = 81, y = 100, p = 181
x = 81, y = 196, p = 277
x = 81, y = 256, p = 337
x = 81, y = 441, p = 522
x = 81, y = 1156, p = 1237
x = 81, y = 1521, p = 1602
x = 100, y = 1, p = 101
x = 100, y = 9, p = 109
x = 100, y = 49, p = 149
x = 100, y = 81, p = 181
x = 100, y = 169, p = 269
x = 100, y = 289, p = 389
x = 100, y = 361, p = 461
x = 100, y = 400, p = 500
x = 100, y = 729, p = 829
x = 100, y = 784, p = 884
x = 100, y = 961, p = 1061
x = 100, y = 1600, p = 1700
x = 121, y = 16, p = 137
x = 121, y = 36, p = 157
x = 121, y = 196, p = 317
x = 121, y = 400, p = 521
x = 121, y = 1156, p = 1277
x = 144, y = 49, p = 193
x = 144, y = 169, p = 313
x = 144, y = 289, p = 433
x = 169, y = 4, p = 173
x = 169, y = 64, p = 233
x = 169, y = 100, p = 269
x = 169, y = 144, p = 313
x = 169, y = 400, p = 569
x = 169, y = 484, p = 653
x = 169, y = 841, p = 1010
x = 169, y = 900, p = 1069
x = 169, y = 1024, p = 1193
x = 169, y = 1444, p = 1613
x = 196, y = 1, p = 197
x = 196, y = 81, p = 277
x = 196, y = 121, p = 317
x = 196, y = 225, p = 421
x = 196, y = 361, p = 557
x = 225, y = 4, p = 229
x = 225, y = 16, p = 241
x = 225, y = 196, p = 421
x = 225, y = 484, p = 709
x = 225, y = 1024, p = 1249
x = 225, y = 1156, p = 1381
x = 225, y = 1444, p = 1669
x = 256, y = 1, p = 257
x = 256, y = 25, p = 281
x = 256, y = 81, p = 337
x = 256, y = 361, p = 617
x = 256, y = 784, p = 1040
x = 256, y = 961, p = 1217
x = 256, y = 1225, p = 1481
x = 289, y = 4, p = 293
x = 289, y = 64, p = 353
x = 289, y = 100, p = 389
x = 289, y = 144, p = 433
x = 289, y = 324, p = 613
x = 289, y = 484, p = 773
x = 289, y = 841, p = 1130
x = 289, y = 1444, p = 1733
x = 324, y = 25, p = 349
x = 324, y = 49, p = 373
x = 324, y = 289, p = 613
x = 324, y = 1225, p = 1549
x = 324, y = 1369, p = 1693
x = 361, y = 36, p = 397
x = 361, y = 100, p = 461
x = 361, y = 196, p = 557
x = 361, y = 256, p = 617
x = 361, y = 400, p = 761
x = 361, y = 576, p = 937
x = 361, y = 841, p = 1202
x = 361, y = 1296, p = 1657
x = 400, y = 1, p = 401
x = 400, y = 9, p = 409
x = 400, y = 49, p = 449
x = 400, y = 121, p = 521
x = 400, y = 169, p = 569
x = 400, y = 361, p = 761
x = 400, y = 729, p = 1129
x = 400, y = 961, p = 1361
x = 400, y = 1089, p = 1489
x = 400, y = 1600, p = 2000
x = 441, y = 16, p = 457
x = 441, y = 100, p = 541
x = 441, y = 441, p = 882
x = 441, y = 676, p = 1117
x = 441, y = 1156, p = 1597
x = 484, y = 25, p = 509
x = 484, y = 169, p = 653
x = 484, y = 225, p = 709
x = 484, y = 289, p = 773
x = 484, y = 729, p = 1213
x = 484, y = 1225, p = 1709
x = 529, y = 64, p = 593
x = 529, y = 144, p = 673
x = 529, y = 324, p = 853
x = 529, y = 400, p = 929
x = 529, y = 484, p = 1013
x = 529, y = 625, p = 1154
x = 529, y = 900, p = 1429
x = 529, y = 1024, p = 1553
x = 529, y = 1444, p = 1973
x = 529, y = 1600, p = 2129
x = 576, y = 1, p = 577
x = 576, y = 25, p = 601
x = 576, y = 361, p = 937
x = 576, y = 1225, p = 1801
x = 625, y = 16, p = 641
x = 625, y = 36, p = 661
x = 625, y = 144, p = 769
x = 625, y = 196, p = 821
x = 625, y = 256, p = 881
x = 625, y = 484, p = 1109
x = 625, y = 529, p = 1154
x = 625, y = 576, p = 1201
x = 625, y = 625, p = 1250
x = 625, y = 676, p = 1301
x = 625, y = 1444, p = 2069
x = 676, y = 1, p = 677
x = 676, y = 25, p = 701
x = 676, y = 81, p = 757
x = 676, y = 121, p = 797
x = 676, y = 784, p = 1460
x = 676, y = 961, p = 1637
x = 676, y = 1225, p = 1901
x = 729, y = 4, p = 733
x = 729, y = 100, p = 829
x = 729, y = 400, p = 1129
x = 729, y = 484, p = 1213
x = 729, y = 1024, p = 1753
x = 784, y = 25, p = 809
x = 784, y = 169, p = 953
x = 784, y = 225, p = 1009
x = 784, y = 784, p = 1568
x = 784, y = 1089, p = 1873
x = 784, y = 1369, p = 2153
x = 841, y = 16, p = 857
x = 841, y = 36, p = 877
x = 841, y = 100, p = 941
x = 841, y = 256, p = 1097
x = 841, y = 900, p = 1741
x = 841, y = 1156, p = 1997
x = 841, y = 1296, p = 2137
x = 841, y = 1600, p = 2441
x = 900, y = 121, p = 1021
x = 900, y = 169, p = 1069
x = 900, y = 961, p = 1861
x = 900, y = 1369, p = 2269
x = 961, y = 16, p = 977
x = 961, y = 36, p = 997
x = 961, y = 100, p = 1061
x = 961, y = 256, p = 1217
x = 961, y = 400, p = 1361
x = 961, y = 529, p = 1490
x = 961, y = 676, p = 1637
x = 961, y = 841, p = 1802
x = 961, y = 900, p = 1861
x = 1024, y = 9, p = 1033
x = 1024, y = 25, p = 1049
x = 1024, y = 169, p = 1193
x = 1024, y = 225, p = 1249
x = 1024, y = 729, p = 1753
x = 1024, y = 1089, p = 2113
x = 1024, y = 1369, p = 2393
x = 1089, y = 4, p = 1093
x = 1089, y = 64, p = 1153
x = 1089, y = 400, p = 1489
x = 1089, y = 1024, p = 2113
x = 1089, y = 1600, p = 2689
x = 1156, y = 25, p = 1181
x = 1156, y = 81, p = 1237
x = 1156, y = 121, p = 1277
x = 1156, y = 225, p = 1381
x = 1156, y = 1225, p = 2381
x = 1156, y = 1521, p = 2677
x = 1225, y = 4, p = 1229
x = 1225, y = 64, p = 1289
x = 1225, y = 256, p = 1481
x = 1225, y = 324, p = 1549
x = 1225, y = 484, p = 1709
x = 1225, y = 529, p = 1754
x = 1225, y = 576, p = 1801
x = 1225, y = 676, p = 1901
x = 1225, y = 1156, p = 2381
x = 1225, y = 1296, p = 2521
x = 1296, y = 1, p = 1297
x = 1296, y = 25, p = 1321
x = 1296, y = 361, p = 1657
x = 1296, y = 1225, p = 2521
x = 1369, y = 4, p = 1373
x = 1369, y = 64, p = 1433
x = 1369, y = 324, p = 1693
x = 1369, y = 625, p = 1994
x = 1369, y = 900, p = 2269
x = 1369, y = 1024, p = 2393
x = 1369, y = 1600, p = 2969
x = 1444, y = 9, p = 1453
x = 1444, y = 49, p = 1493
x = 1444, y = 169, p = 1613
x = 1444, y = 225, p = 1669
x = 1444, y = 289, p = 1733
x = 1444, y = 625, p = 2069
x = 1521, y = 100, p = 1621
x = 1521, y = 256, p = 1777
x = 1521, y = 1156, p = 2677
x = 1521, y = 1600, p = 3121
x = 1600, y = 1, p = 1601
x = 1600, y = 9, p = 1609
x = 1600, y = 121, p = 1721
x = 1600, y = 289, p = 1889
x = 1600, y = 784, p = 2384
x = 1600, y = 1089, p = 2689
x = 1600, y = 1369, p = 2969
x = 1600, y = 1521, p = 3121