Inhaltsverzeichnis

Development of
Algorithmic Constructions

english

Beschreibung

Alle Primzahlen, die die Form 4*k+1 haben, liegen auf dem Polynom x^3+x^2+x+1.
Die ersten Primzahlen dieses Typs sind:

5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233,
241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397, 401

                                        2
                                 1, 4, 2

                                2, 15, 3 5

                                        3
                                3, 40, 2  5

                                4, 85, 5 17

                                       2
                              5, 156, 2  3 13

                               6, 259, 7 37

                                        4  2
                               7, 400, 2  5

                                       2
                              8, 585, 3  5 13

                                       2
                              9, 820, 2  5 41

                             10, 1111, 11 101

                                        3
                             11, 1464, 2  3 61

                             12, 1885, 5 13 29

                                       2
                            13, 2380, 2  5 7 17

                             14, 2955, 3 5 197

                                        5
                             15, 3616, 2  113

                             16, 4369, 17 257

                                      2  2
                           17, 5220, 2  3  5 29

                                       2
                            18, 6175, 5  13 19

                                       3
                            19, 7240, 2  5 181

                             20, 8421, 3 7 401

                                      2
                           21, 9724, 2  11 13 17

                            22, 11155, 5 23 97

                                       4
                           23, 12720, 2  3 5 53

                                         2
                             24, 14425, 5  577

                                       2
                           25, 16276, 2  13 313

                                         3
                             26, 18279, 3  677

                                       3
                           27, 20440, 2  5 7 73

                            28, 22765, 5 29 157

                                       2
                           29, 25260, 2  3 5 421

                            30, 27931, 17 31 53

                                        6
                            31, 30784, 2  13 37

                                         2
                           32, 33825, 3 5  11 41

                                      2
                          33, 37060, 2  5 17 109

                           34, 40495, 5 7 13 89

                                       3  2
                           35, 44136, 2  3  613

                            36, 47989, 37 1297

                                      2
                          37, 52060, 2  5 19 137

                                               2
                           38, 56355, 3 5 13 17

                                        4
                            39, 60880, 2  5 761

                            40, 65641, 41 1601

                                       2       2
                           41, 70644, 2  3 7 29

                            42, 75895, 5 43 353

                                      3  2
                          43, 81400, 2  5  11 37

                                      2
                          44, 87165, 3  5 13 149

                                       2
                           45, 93196, 2  23 1013

                            46, 99499, 29 47 73

                                      5
                         47, 106080, 2  3 5 13 17

                                          2
                           48, 112945, 5 7  461

                                       2  2
                          49, 120100, 2  5  1201

                          50, 127551, 3 17 41 61

                                       3
                          51, 135304, 2  13 1301

                           52, 143365, 5 53 541

                                       2  3
                          53, 151740, 2  3  5 281

                           54, 160435, 5 11 2917

                                       4
                          55, 169456, 2  7 17 89

                           56, 178809, 3 19 3137

                                       2  3
                          57, 188500, 2  5  13 29

                           58, 198535, 5 59 673

                                       3
                          59, 208920, 2  3 5 1741

                           60, 219661, 13 61 277

                                       2
                          61, 230764, 2  31 1861

                                       2
                          62, 242235, 3  5 7 769

                                        7
                           63, 254080, 2  5 397

                          64, 266305, 5 13 17 241

                                      2
                         65, 278916, 2  3 11 2113

                            66, 291919, 67 4357

                                       3
                          67, 305320, 2  5 17 449

                                         3
                          68, 319125, 3 5  23 37

                                       2
                          69, 333340, 2  5 7 2381

                                         2
                           70, 347971, 13  29 71

                                       4  2
                          71, 363024, 2  3  2521

                          72, 378505, 5 17 61 73

                                      2
                         73, 394420, 2  5 13 37 41

                                          2
                           74, 410775, 3 5  5477

                                       3
                          75, 427576, 2  19 29 97

                          76, 444829, 7 11 53 109

                                      2
                         77, 462540, 2  3 5 13 593

                           78, 480715, 5 79 1217

                                        5
                           79, 499360, 2  5 3121

                                        4
                           80, 518481, 3  37 173

                                      2
                         81, 538084, 2  17 41 193

                                        2
                           82, 558175, 5  83 269

                                     3
                        83, 578760, 2  3 5 7 13 53

                           84, 599845, 5 17 7057

                                       2
                          85, 621436, 2  43 3613

                          86, 643539, 3 13 29 569

                                       4
                          87, 666160, 2  5 11 757

                           88, 689305, 5 89 1549

                                     2  2
                        89, 712980, 2  3  5 17 233

                           90, 737191, 7 13 8101

                                      3
                         91, 761944, 2  23 41 101

                          92, 787245, 3 5 31 1693

                                      2  2
                         93, 813100, 2  5  47 173

                           94, 839515, 5 19 8837

                                        6
                           95, 866496, 2  3 4513

                           96, 894049, 13 97 709

                                       2    2
                          97, 922180, 2  5 7  941

                                     2
                        98, 950895, 3  5 11 17 113

                                      3  2   2
                         99, 980200, 2  5  13  29

                         100, 1010101, 73 101 137