Números Primos (de la Criba de Eratóstenes a la de Aschero)
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Se trata de la Criba creada por el Doctor Sergio Aschero que supera al modelo de Eratóstenes.
Transcript of Números Primos (de la Criba de Eratóstenes a la de Aschero)
Sergio Aschero NMEROS PRIMOS. DE LA CRIBA DE ERATOSTENES A LA CRIBA DE ASCHERO: LA EVOLUCIN DE UN MODELO MATEMTICO Resumen La Criba de Aschero presenta un modelo matemtico que supera al de la Criba de Eratstenes, obteniendo un resultado similar con respecto a la obtencin de nmeros primos y eliminacin de nmeros compuestos pero con una mayor simplicidad operativa. Criba de Eratstenes La Criba de Eratstenes es un procedimiento para determinar todos los nmeros primos hasta cierto nmero natural dado. Esto se hace recorriendo una tabla de nmeros usando el siguiente algoritmo para los 1000 primeros nmeros naturales:
Empezamos en el nmero 2, resaltamos el nmero 2 como primo pero desechamos todos los mltiplos de 2 (es decir, desechamos 4, 6, 8, etc.). Se continua con el siguiente nmero no desechado en la tabla, en este caso el nmero 3, resaltamos el nmero 3 como primo y desechamos todos los mltiplos de 3 (es decir desechamos 6, 9, 12, etc.). El siguiente nmero no desechado en la tabla es el 5, resaltamos el nmero 5 como primo y todos los mltiplos de 5 (es decir desechamos 10, 15, 20, etc.). Y as, paso a paso se tachan todos los nmeros que no son primos.
El proceso termina cuando el cuadrado del mayor nmero confirmado como primo es menor que el nmero final de la lista.
Criba de Eratstenes para los primeros 1000 nmeros naturales 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400
401 411 421 431 441 451 461 471 481 491 501 511 521 531 541 551 561 571 581 591 601 611 621 631 641 651 661 671 681 691 701 711 721 731 741 751 761 771 781 791 801
402 412 422 432 442 452 462 472 482 492 502 512 522 532 542 552 562 572 582 592 602 612 622 632 642 652 662 672 682 692 702 712 722 732 742 752 762 772 782 792 802
403 413 423 433 443 453 463 473 483 493 503 513 523 533 543 553 563 573 583 593 603 613 623 633 643 653 663 673 683 693 703 713 723 733 743 753 763 773 783 793 803
404 414 424 434 444 454 464 474 484 494 504 514 524 534 544 554 564 574 584 594 604 614 624 634 644 654 664 674 684 694 704 714 724 734 744 754 764 774 784 794 804
405 415 425 435 445 455 465 475 485 495 505 515 525 535 545 555 565 575 585 595 605 615 625 635 645 655 665 675 685 695 705 715 725 735 745 755 765 775 785 795 805
406 416 426 436 446 456 466 476 486 496 506 516 526 536 546 556 566 576 586 596 606 616 626 636 646 656 666 676 686 696 706 716 726 736 746 756 766 776 786 796 806
407 417 427 437 447 457 467 477 487 497 507 517 527 537 547 557 567 577 587 597 607 617 627 637 647 657 667 677 687 697 707 717 727 737 747 757 767 777 787 797 807
408 418 428 438 448 458 468 478 488 498 508 518 528 538 548 558 568 578 588 598 608 618 628 638 648 658 668 678 688 698 708 718 728 738 748 758 768 778 788 798 808
409 419 429 439 449 459 469 479 489 499 509 519 529 539 549 559 569 579 589 599 609 619 629 639 649 659 669 679 689 699 709 719 729 739 749 759 769 779 789 799 809
410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810
811 821 831 841 851 861 871 881 891 901 911 921 931 941 951 961 971 981 991
812 822 832 842 852 862 872 882 892 902 912 922 932 942 952 962 972 982 992
813 823 833 843 853 863 873 883 893 903 913 923 933 943 953 963 973 983 993
814 824 834 844 854 864 874 884 894 904 914 924 934 944 954 964 974 984 994
815 825 835 845 855 865 875 885 895 905 915 925 935 945 955 965 975 985 995
816 826 836 846 856 866 876 886 896 906 916 926 936 946 956 966 976 986 996
817 827 837 847 857 867 877 887 897 907 917 927 937 947 957 967 977 987 997
818 828 838 848 858 868 878 888 898 908 918 928 938 948 958 968 978 988 998
819 829 839 849 859 869 879 889 899 909 919 929 939 949 959 969 979 989 999
820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000
Con la Criba de Eratstenes es necesario contar (en este anlisis) con 1000 nmeros naturales para llegar a los168 nmeros primos que figuran en la lista coloreados de amarillo. Anlisis numeral Veamos a continuacin los 1000 nmeros primos y compuestos con todas sus caractersticas:
1 = {1} (1 divisor) 2 = {2} (NUMERO PRIMO) 3 = {3} (NUMERO PRIMO) 4 = {2, 4} (2 divisores) 5 = {5} (NUMERO PRIMO) 6 = {2, 3, 6} (3 divisores) 7 = {7} (NUMERO PRIMO) 8 = {2, 4, 8} (3 divisores)
9 = {3, 9} (2 divisores) 10 = {2, 5, 10} (3 divisores) 11 = {11} (NUMERO PRIMO) 12 = {2, 3, 4, 6, 12} (5 divisores) 13 = {13} (NUMERO PRIMO) 14 = {2, 7, 14} (3 divisores) 15 = {3, 5, 15} (3 divisores) 16 = {2, 4, 8, 16} (4 divisores) 17 = {17} (NUMERO PRIMO) 18 = {2, 3, 6, 9, 18} (5 divisores) 19 = {19} (NUMERO PRIMO) 20 = {2, 4, 5, 10, 20} (5 divisores) 21 = {3, 7, 21} (3 divisores) 22 = {2, 11, 22} (3 divisores) 23 = {23} (NUMERO PRIMO) 24 = {2, 3, 4, 6, 8, 12, 24} (7 divisores) 25 = {5, 25} (2 divisores) 26 = {2, 13, 26} (3 divisores) 27 = {3, 9, 27} (3 divisores) 28 = {2, 4, 7, 14, 28} (5 divisores) 29 = {29} (NUMERO PRIMO) 30 = {2, 3, 5, 6, 10, 15, 30} (7 divisores) 31 = {31} (PRIMO NUMERO) 32 = {2, 4, 8, 16, 32} (5 divisores) 33 = {3, 11, 33} (3 divisores) 34 = {2, 17, 34} (3 divisores) 35 = {5, 7, 35} (3 divisores) 36 = {2, 3, 4, 6, 9, 12, 18, 36} (8 divisores) 37 = {37} (NUMERO PRIMO) 38 = {2, 19, 38} (3 divisores) 39 = {3, 13, 39} (3 divisores) 40 = {2, 4, 5, 8, 10, 20, 40} (7 divisores) 41 = {41} (NUMERO PRIMO) 42 = {2, 3, 6, 7, 14, 21, 42} (7 divisores) 43 = {43} (NUMERO PRIMO) 44 = {2, 4, 11, 22, 44} (5 divisores) 45 = {3, 5, 9, 15, 45} (5 divisores) 46 = {2, 23, 46} (3 divisores) 47 = {47} (NUMERO PRIMO) 48 = {2, 3, 4, 6, 8, 12, 16, 24, 48} (9 divisores) 49 = {7, 49} (2 divisores)
50 = {2, 5, 10, 25, 50} (5 divisores) 51 = {3, 17, 51} (3 divisores) 52 = {2, 4, 13, 26, 52} (5 divisores) 53 = {53} (NUMERO PRIMO) 54 = {2, 3, 6, 9, 18, 27, 54} (7 divisores) 55 = {5, 11, 55} (3 divisores) 56 = {2, 4, 7, 8, 14, 28, 56} (7 divisores) 57 = {3, 19, 57} (3 divisores) 58 = {2, 29, 58} (3 divisores) 59 = {59} (NUMERO PRIMO) 60 = {2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60} (11 divisores) 61 = {61} (NUMERO PRIMO) 62 = {2, 31, 62} (3 divisores) 63 = {3, 7, 9, 21, 63} (5 divisores) 64 = {2, 4, 8, 16, 32, 64} (6 divisores) 65 = {5, 13, 65} (3 divisores) 66 = {2, 3, 6, 11, 22, 33, 66} (7 divisores) 67 = {67} (NUMERO PRIMO) 68 = {2, 4, 17, 34, 68} (5 divisores) 69 = {3, 23, 69} (3 divisores) 70 = {2, 5, 7, 10, 14, 35, 70} (7 divisores) 71 = {71} (NUMERO PRIMO) 72 = {2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72} (11 divisores) 73 = {73} (NUMERO PRIMO) 74 = {2, 37, 74} (3 divisores) 75 = {3, 5, 15, 25, 75} (5 divisores) 76 = {2, 4, 19, 38, 76} (5 divisores) 77 = {7, 11, 77} (3 divisores) 78 = {2, 3, 6, 13, 26, 39, 78} (7 divisores) 79 = {79} (NUMERO PRIMO) 80 = {2, 4, 5, 8, 10, 16, 20, 40, 80} (9 divisores) 81 = {3, 9, 27, 81} (4 divisores) 82 = {2, 41, 82} (3 divisores) 83 = {83} (PRIMO NUMERO) 84 = {2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84} (11 divisores) 85 = {5, 17, 85} (3 divisores) 86 = {2, 43, 86} (3 divisores) 87 = {3, 29, 87} (3 divisores) 88 = {2, 4, 8, 11, 22, 44, 88} (7 divisores) 89 = {89} (PRIMO NUMERO) 90 = {2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90} (11 divisores)
91 = {7, 13, 91} (3 divisores) 92 = {2, 4, 23, 46, 92} (5 divisores) 93 = {3, 31, 93} (3 divisores) 94 = {2, 47, 94} (3 divisores) 95 = {5, 19, 95} (3 divisores) 96 = {2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96} (11 divisores) 97 = {97} (NUMERO PRIMO) 98 = {2, 7, 14, 49, 98} (5 divisores) 99 = {3, 9, 11, 33, 99} (5 divisores) 100 = {2, 4, 5, 10, 20, 25, 50, 100} (8 divisores) 101 = {101} (NUMERO PRIMO) 102 = {2, 3, 6, 17, 34, 51, 102} (7 divisores) 103 = {103} (NUMERO PRIMO) 104 = {2, 4, 8, 13, 26, 52, 104} (7 divisores) 105 = {3, 5, 7, 15, 21, 35, 105} (7 divisores) 106 = {2, 53, 106} (3 divisores) 107 = {107} (NUMERO PRIMO) 108 = {2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108} (11 divisores) 109 = {109} (NUMERO PRIMO) 110 = {2, 5, 10, 11, 22, 55, 110} (7 divisores) 111 = {3, 37, 111} (3 divisores) 112 = {2, 4, 7, 8, 14, 16, 28, 56, 112} (9 divisores) 113 = {113} (NUMERO PRIMO) 114 = {2, 3, 6, 19, 38, 57, 114} (7 divisores) 115 = {5, 23, 115} (3 divisores) 116 = {2, 4, 29, 58, 116} (5 divisores) 117 = {3, 9, 13, 39, 117} (5 divisores) 118 = {2, 59, 118} (3 divisores) 119 = {7, 17, 119} (3 divisores) 120 = {2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120} (15 divisores) 121 = {11, 121} (2 divisores) 122 = {2, 61, 122} (3 divisores) 123 = {3, 41, 123} (3 divisores) 124 = {2, 4, 31, 62, 124} (5 divisores) 125 = {5, 25, 125} (3 divisores) 126 = {2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126} (11 divisores) 127 = {127} (NUMERO PRIMO) 128 = {2, 4, 8, 16, 32, 64, 128} (7 divisores) 129 = {3, 43, 129} (3 divisores) 130 = {2, 5, 10, 13, 26, 65, 130} (7 divisores) 131 = {131} (NUMERO PRIMO)
132 = {2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132} (11 divisores) 133 = {7, 19, 133} (3 divisores) 134 = {2, 67, 134} (3 divisores) 135 = {3, 5, 9, 15, 27, 45, 135} (7 divisores) 136 = {2, 4, 8, 17, 34, 68, 136} (7 divisores) 137 = {137} (NUMERO PRIMO) 138 = {2, 3, 6, 23, 46, 69, 138} (7 divisores) 139 = {139} (NUMERO PRIMO) 140 = {2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140} (11 divisores) 141 = {3, 47, 141} (3 divisores) 142 = {2, 71, 142} (3 divisores) 143 = {11, 13, 143} (3 divisores) 144 = {2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144} (14 divisores) 145 = {5, 29, 145} (3 divisores) 146 = {2, 73, 146} (3 divisores) 147 = {3, 7, 21, 49, 147} (5 divisores) 148 = {2, 4, 37, 74, 148} (5 divisores) 149 = {149} (NUMERO PRIMO) 150 = {2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150} (11 divisores) 151 = {151} (NUMERO PRIMO) 152 = {2, 4, 8, 19, 38, 76, 152} (7 divisores) 153 = {3, 9, 17, 51, 153} (5 divisores) 154 = {2, 7, 11, 14, 22, 77, 154} (7 divisores) 155 = {5, 31, 155} (3 divisores) 156 = {2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156} (11 divisores) 157 = {157} (NUMERO PRIMO) 158 = {2, 79, 158} (3 divisores) 159 = {3, 53, 159} (3 divisores) 160 = {2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160} (11 divisores) 161 = {7, 23, 161} (3 divisores) 162 = {2, 3, 6, 9, 18, 27, 54, 81, 162} (9 divisores) 163 = {163} (NUMERO PRIMO) 164 = {2, 4, 41, 82, 164} (5 divisores) 165 = {3, 5, 11, 15, 33, 55, 165} (7 divisores) 166 = {2, 83, 166} (3 divisores) 167 = {167} (NUMERO PRIMO) 168 = {2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168} (15 divisores) 169 = {13, 169} (2 divisores) 170 = {2, 5, 10, 17, 34, 85, 170} (7 divisores) 171 = {3, 9, 19, 57, 171} (5 divisores) 172 = {2, 4, 43, 86, 172} (5 divisores)
173 = {173} (NUMERO PRIMO) 174 = {2, 3, 6, 29, 58, 87, 174} (7 divisores) 175 = {5, 7, 25, 35, 175} (5 divisores) 176 = {2, 4, 8, 11, 16, 22, 44, 88, 176} (9 divisores) 177 = {3, 59, 177} (3 divisores) 178 = {2, 89, 178} (3 divisores) 179 = {179} (NUMERO PRIMO) 180 = {2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180} (17 divisores) 181 = {181} (NUMERO PRIMO) 182 = {2, 7, 13, 14, 26, 91, 182} (7 divisores) 183 = {3, 61, 183} (3 divisores) 184 = {2, 4, 8, 23, 46, 92, 184} (7 divisores) 185 = {5, 37, 185} (3 divisores) 186 = {2, 3, 6, 31, 62, 93, 186} (7 divisores) 187 = {11, 17, 187} (3 divisores) 188 = {2, 4, 47, 94, 188} (5 divisores) 189 = {3, 7, 9, 21, 27, 63, 189} (7 divisores) 190 = {2, 5, 10, 19, 38, 95, 190} (7 divisores) 191 = {191} (NUMERO PRIMO) 192 = {2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192} (13 divisores) 193 = {193} (NUMERO PRIMO) 194 = {2, 97, 194} (3 divisores) 195 = {3, 5, 13, 15, 39, 65, 195} (7 divisores) 196 = {2, 4, 7, 14, 28, 49, 98, 196} (8 divisores) 197 = {197} (NUMERO PRIMO) 198 = {2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198} (11 divisores) 199 = {199} (NUMERO PRIMO) 200 = {2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200} (11 divisores) 201 = {3, 67, 201} (3 divisores) 202 = {2, 101, 202} (3 divisores) 203 = {7, 29, 203} (3 divisores) 204 = {2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204} (11 divisores) 205 = {5, 41, 205} (3 divisores) 206 = {2, 103, 206} (3 divisores) 207 = {3, 9, 23, 69, 207} (5 divisores) 208 = {2, 4, 8, 13, 16, 26, 52, 104, 208} (9 divisores) 209 = {11, 19, 209} (3 divisores) 210 = {2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210} (15 divisores) 211 = {211} (NUMERO PRIMO)
212 = {2, 4, 53, 106, 212} (5 divisores) 213 = {3, 71, 213} (3 divisores) 214 = {2, 107, 214} (3 divisores) 215 = {5, 43, 215} (3 divisores) 216 = {2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216} (15 divisores) 217 = {7, 31, 217} (3 divisores) 218 = {2, 109, 218} (3 divisores) 219 = {3, 73, 219} (3 divisores) 220 = {2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220} (11 divisores) 221 = {13, 17, 221} (3 divisores) 222 = {2, 3, 6, 37, 74, 111, 222} (7 divisores) 223 = {223} (NUMERO PRIMO) 224 = {2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224} (11 divisores) 225 = {3, 5, 9, 15, 25, 45, 75, 225} (8 divisores) 226 = {2, 113, 226} (3 divisores) 227 = {227} (NUMERO PRIMO) 228 = {2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228} (11 divisores) 229 = {229} (NUMERO PRIMO) 230 = {2, 5, 10, 23, 46, 115, 230} (7 divisores) 231 = {3, 7, 11, 21, 33, 77, 231} (7 divisores) 232 = {2, 4, 8, 29, 58, 116, 232} (7 divisores) 233 = {233} (NUMERO PRIMO) 234 = {2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234} (11 divisores) 235 = {5, 47, 235} (3 divisores) 236 = {2, 4, 59, 118, 236} (5 divisores) 237 = {3, 79, 237} (3 divisores) 238 = {2, 7, 14, 17, 34, 119, 238} (7 divisores) 239 = {239} (NUMERO PRIMO) 240 = {2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240} (19 divisores) 241 = {241} (NUMERO PRIMO) 242 = {2, 11, 22, 121, 242} (5 divisores) 243 = {3, 9, 27, 81, 243} (5 divisores) 244 = {2, 4, 61, 122, 244} (5 divisores) 245 = {5, 7, 35, 49, 245} (5 divisores) 246 = {2, 3, 6, 41, 82, 123, 246} (7 divisores) 247 = {13, 19, 247} (3 divisores) 248 = {2, 4, 8, 31, 62, 124, 248} (7 divisores) 249 = {3, 83, 249} (3 divisores) 250 = {2, 5, 10, 25, 50, 125, 250} (7 divisores) 251 = {251} (NUMERO PRIMO)
252 = {2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252} (17 divisores) 253 = {11, 23, 253} (3 divisores) 254 = {2, 127, 254} (3 divisores) 255 = {3, 5, 15, 17, 51, 85, 255} (7 divisores) 256 = {2, 4, 8, 16, 32, 64, 128, 256} (8 divisores) 257 = {257} (NUMERO PRIMO) 258 = {2, 3, 6, 43, 86, 129, 258} (7 divisores) 259 = {7, 37, 259} (3 divisores) 260 = {2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260} (11 divisores) 261 = {3, 9, 29, 87, 261} (5 divisores) 262 = {2, 131, 262} (3 divisores) 263 = {263} (NUMERO PRIMO) 264 = {2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264} (15 divisores) 265 = {5, 53, 265} (3 divisores) 266 = {2, 7, 14, 19, 38, 133, 266} (7 divisores) 267 = {3, 89, 267} (3 divisores) 268 = {2, 4, 67, 134, 268} (5 divisores) 269 = {269} (NUMERO PRIMO) 270 = {2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270} (15 divisores) 271 = {271} (NUMERO PRIMO) 272 = {2, 4, 8, 16, 17, 34, 68, 136, 272} (9 divisores) 273 = {3, 7, 13, 21, 39, 91, 273} (7 divisores) 274 = {2, 137, 274} (3 divisores) 275 = {5, 11, 25, 55, 275} (5 divisores) 276 = {2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276} (11 divisores) 277 = {277} (NUMERO PRIMO) 278 = {2, 139, 278} (3 divisores) 279 = {3, 9, 31, 93, 279} (5 divisores) 280 = {2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280} (15 divisores) 281 = {281} (NUMERO PRIMO) 282 = {2, 3, 6, 47, 94, 141, 282} (7 divisores) 283 = {283} (NUMERO PRIMO) 284 = {2, 4, 71, 142, 284} (5 divisores) 285 = {3, 5, 15, 19, 57, 95, 285} (7 divisores) 286 = {2, 11, 13, 22, 26, 143, 286} (7 divisores) 287 = {7, 41, 287} (3 divisores) 288 = {2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288} (17
divisores) 289 = {17, 289} (2 divisores) 290 = {2, 5, 10, 29, 58, 145, 290} (7 divisores) 291 = {3, 97, 291} (3 divisores) 292 = {2, 4, 73, 146, 292} (5 divisores) 293 = {293} (NUMERO PRIMO) 294 = {2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294} (11 divisores) 295 = {5, 59, 295} (3 divisores) 296 = {2, 4, 8, 37, 74, 148, 296} (7 divisores) 297 = {3, 9, 11, 27, 33, 99, 297} (7 divisores) 298 = {2, 149, 298} (3 divisores) 299 = {13, 23, 299} (3 divisores) 300 = {2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300} (17 divisores) 301 = {7, 43, 301} (3 divisores) 302 = {2, 151, 302} (3 divisores) 303 = {3, 101, 303} (3 divisores) 304 = {2, 4, 8, 16, 19, 38, 76, 152, 304} (9 divisores) 305 = {5, 61, 305} (3 divisores) 306 = {2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306} (11 divisores) 307 = {307} (NUMERO PRIMO) 308 = {2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308} (11 divisores) 309 = {3, 103, 309} (3 divisores) 310 = {2, 5, 10, 31, 62, 155, 310} (7 divisores) 311 = {311} (NUMERO PRIMO) 312 = {2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312} (15 divisores) 313 = {313} (NUMERO PRIMO) 314 = {2, 157, 314} (3 divisores) 315 = {3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315} (11 divisores) 316 = {2, 4, 79, 158, 316} (5 divisores) 317 = {317} (NUMERO PRIMO) 318 = {2, 3, 6, 53, 106, 159, 318} (7 divisores) 319 = {11, 29, 319} (3 divisores) 320 = {2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320} (13 divisores) 321 = {3, 107, 321} (3 divisores) 322 = {2, 7, 14, 23, 46, 161, 322} (7 divisores) 323 = {17, 19, 323} (3 divisores) 324 = {2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324} (14 divisores) 325 = {5, 13, 25, 65, 325} (5 divisores) 326 = {2, 163, 326} (3 divisores)
327 = {3, 109, 327} (3 divisores) 328 = {2, 4, 8, 41, 82, 164, 328} (7 divisores) 329 = {7, 47, 329} (3 divisores) 330 = {2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330} (15 divisores) 331 = {331} (NUMERO PRIMO) 332 = {2, 4, 83, 166, 332} (5 divisores) 333 = {3, 9, 37, 111, 333} (5 divisores) 334 = {2, 167, 334} (3 divisores) 335 = {5, 67, 335} (3 divisores) 336 = {2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336} (19 divisores) 337 = {337} (NUMERO PRIMO) 338 = {2, 13, 26, 169, 338} (5 divisores) 339 = {3, 113, 339} (3 divisores) 340 = {2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340} (11 divisores) 341 = {11, 31, 341} (3 divisores) 342 = {2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342} (11 divisores) 343 = {7, 49, 343} (3 divisores) 344 = {2, 4, 8, 43, 86, 172, 344} (7 divisores) 345 = {3, 5, 15, 23, 69, 115, 345} (7 divisores) 346 = {2, 173, 346} (3 divisores) 347 = {347} (NUMERO PRIMO) 348 = {2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348} (11 divisores) 349 = {349} (NUMERO PRIMO) 350 = {2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350} (11 divisores) 351 = {3, 9, 13, 27, 39, 117, 351} (7 divisores) 352 = {2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352} (11 divisores) 353 = {353} (NUMERO PRIMO) 354 = {2, 3, 6, 59, 118, 177, 354} (7 divisores) 355 = {5, 71, 355} (3 divisores) 356 = {2, 4, 89, 178, 356} (5 divisores) 357 = {3, 7, 17, 21, 51, 119, 357} (7 divisores) 358 = {2, 179, 358} (3 divisores) 359 = {359} (NUMERO PRIMO) 360 = {2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360} ( 23 divisores) 361 = {19, 361} (2 divisores) 362 = {2, 181, 362} (3 divisores) 363 = {3, 11, 33, 121, 363} (5 divisores) 364 = {2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364} (11 divisores)
365 = {5, 73, 365} (3 divisores) 366 = {2, 3, 6, 61, 122, 183, 366} (7 divisores) 367 = {367} (NUMERO PRIMO) 368 = {2, 4, 8, 16, 23, 46, 92, 184, 368} (9 divisores) 369 = {3, 9, 41, 123, 369} (5 divisores) 370 = {2, 5, 10, 37, 74, 185, 370} (7 divisores) 371 = {7, 53, 371} (3 divisores) 372 = {2, 3, 4, 6, 12, 31, 62, 93, 124, 186, 372} (11 divisores) 373 = {373} (NUMERO PRIMO) 374 = {2, 11, 17, 22, 34, 187, 374} (7 divisores) 375 = {3, 5, 15, 25, 75, 125, 375} (7 divisores) 376 = {2, 4, 8, 47, 94, 188, 376} (7 divisores) 377 = {13, 29, 377} (3 divisores) 378 = {2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378} (15 divisores) 379 = {379} (NUMERO PRIMO) 380 = {2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380} (11 divisores) 381 = {3, 127, 381} (3 divisores) 382 = {2, 191, 382} (3 divisores) 383 = {383} (NUMERO PRIMO) 384 = {2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384} (15 divisores) 385 = {5, 7, 11, 35, 55, 77, 385} (7 divisores) 386 = {2, 193, 386} (3 divisores) 387 = {3, 9, 43, 129, 387} (5 divisores) 388 = {2, 4, 97, 194, 388} (5 divisores) 389 = {389} (NUMERO PRIMO) 390 = {2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390} (15 divisores) 391 = {17, 23, 391} (3 divisores) 392 = {2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392} (11 divisores) 393 = {3, 131, 393} (3 divisores) 394 = {2, 197, 394} (3 divisores) 395 = {5, 79, 395} (3 divisores) 396 = {2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396} (17 divisores) 397 = {397} (NUMERO PRIMO) 398 = {2, 199, 398} (3 divisores) 399 = {3, 7, 19, 21, 57, 133, 399} (7 divisores) 400 = {2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400} (14 divisores) 401 = {401} (NUMERO PRIMO)
402 = {2, 3, 6, 67, 134, 201, 402} (7 divisores) 403 = {13, 31, 403} (3 divisores) 404 = {2, 4, 101, 202, 404} (5 divisores) 405 = {3, 5, 9, 15, 27, 45, 81, 135, 405} (9 divisores) 406 = {2, 7, 14, 29, 58, 203, 406} (7 divisores) 407 = {11, 37, 407} (3 divisores) 408 = {2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408} (15 divisores) 409 = {409} (NUMERO PRIMO) 410 = {2, 5, 10, 41, 82, 205, 410} (7 divisores) 411 = {3, 137, 411} (3 divisores) 412 = {2, 4, 103, 206, 412} (5 divisores) 413 = {7, 59, 413} (3 divisores) 414 = {2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414} (11 divisores) 415 = {5, 83, 415} (3 divisores) 416 = {2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416} (11 divisores) 417 = {3, 139, 417} (3 divisores) 418 = {2, 11, 19, 22, 38, 209, 418} (7 divisores) 419 = {419} (NUMERO PRIMO) 420 = {2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420} ( 23 divisores) 421 = {421} (NUMERO PRIMO) 422 = {2, 211, 422} (3 divisores) 423 = {3, 9, 47, 141, 423} (5 divisores) 424 = {2, 4, 8, 53, 106, 212, 424} (7 divisores) 425 = {5, 17, 25, 85, 425} (5 divisores) 426 = {2, 3, 6, 71, 142, 213, 426} (7 divisores) 427 = {7, 61, 427} (3 divisores) 428 = {2, 4, 107, 214, 428} (5 divisores) 429 = {3, 11, 13, 33, 39, 143, 429} (7 divisores) 430 = {2, 5, 10, 43, 86, 215, 430} (7 divisores) 431 = {431} (NUMERO PRIMO) 432 = {2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432} (19 divisores) 433 = {433} (NUMERO PRIMO) 434 = {2, 7, 14, 31, 62, 217, 434} (7 divisores) 435 = {3, 5, 15, 29, 87, 145, 435} (7 divisores) 436 = {2, 4, 109, 218, 436} (5 divisores) 437 = {19, 23, 437} (3 divisores) 438 = {2, 3, 6, 73, 146, 219, 438} (7 divisores) 439 = {439} (NUMERO PRIMO)
440 = {2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440} (15 divisores) 441 = {3, 7, 9, 21, 49, 63, 147, 441} (8 divisores) 442 = {2, 13, 17, 26, 34, 221, 442} (7 divisores) 443 = {443} (NUMERO PRIMO) 444 = {2, 3, 4, 6, 12, 37, 74, 111, 148, 222, 444} (11 divisores) 445 = {5, 89, 445} (3 divisores) 446 = {2, 223, 446} (3 divisores) 447 = {3, 149, 447} (3 divisores) 448 = {2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 224, 448} (13 divisores) 449 = {449} (NUMERO PRIMO) 450 = {2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450} (17 divisores) 451 = {11, 41, 451} (3 divisores) 452 = {2, 4, 113, 226, 452} (5 divisores) 453 = {3, 151, 453} (3 divisores) 454 = {2, 227, 454} (3 divisores) 455 = {5, 7, 13, 35, 65, 91, 455} (7 divisores) 456 = {2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456} (15 divisores) 457 = {457} (NUMERO PRIMO) 458 = {2, 229, 458} (3 divisores) 459 = {3, 9, 17, 27, 51, 153, 459} (7 divisores) 460 = {2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460} (11 divisores) 461 = {461} (NUMERO PRIMO) 462 = {2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462} (15 divisores) 463 = {463} (NUMERO PRIMO) 464 = {2, 4, 8, 16, 29, 58, 116, 232, 464} (9 divisores) 465 = {3, 5, 15, 31, 93, 155, 465} (7 divisores) 466 = {2, 233, 466} (3 divisores) 467 = {467} (NUMERO PRIMO) 468 = {2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468} (17 divisores) 469 = {7, 67, 469} (3 divisores) 470 = {2, 5, 10, 47, 94, 235, 470} (7 divisores) 471 = {3, 157, 471} (3 divisores) 472 = {2, 4, 8, 59, 118, 236, 472} (7 divisores) 473 = {11, 43, 473} (3 divisores) 474 = {2, 3, 6, 79, 158, 237, 474} (7 divisores) 475 = {5, 19, 25, 95, 475} (5 divisores)
476 = {2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476} (11 divisores) 477 = {3, 9, 53, 159, 477} (5 divisores) 478 = {2, 239, 478} (3 divisores) 479 = {479} (NUMERO PRIMO) 480 = {2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480} ( 23 divisores) 481 = {13, 37, 481} (3 divisores) 482 = {2, 241, 482} (3 divisores) 483 = {3, 7, 21, 23, 69, 161, 483} (7 divisores) 484 = {2, 4, 11, 22, 44, 121, 242, 484} (8 divisores) 485 = {5, 97, 485} (3 divisores) 486 = {2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486} (11 divisores) 487 = {487} (NUMERO PRIMO) 488 = {2, 4, 8, 61, 122, 244, 488} (7 divisores) 489 = {3, 163, 489} (3 divisores) 490 = {2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490} (11 divisores) 491 = {491} (NUMERO PRIMO) 492 = {2, 3, 4, 6, 12, 41, 82, 123, 164, 246, 492} (11 divisores) 493 = {17, 29, 493} (3 divisores) 494 = {2, 13, 19, 26, 38, 247, 494} (7 divisores) 495 = {3, 5, 9, 11, 15, 33, 45, 55, 99, 165, 495} (11 divisores) 496 = {2, 4, 8, 16, 31, 62, 124, 248, 496} (9 divisores) 497 = {7, 71, 497} (3 divisores) 498 = {2, 3, 6, 83, 166, 249, 498} (7 divisores) 499 = {499} (NUMERO PRIMO) 500 = {2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500} (11 divisores) 501 = {3, 167, 501} (3 divisores) 502 = {2, 251, 502} (3 divisores) 503 = {503} (NUMERO PRIMO) 504 = {2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504} ( 23 divisores) 505 = {5, 101, 505} (3 divisores) 506 = {2, 11, 22, 23, 46, 253, 506} (7 divisores) 507 = {3, 13, 39, 169, 507} (5 divisores) 508 = {2, 4, 127, 254, 508} (5 divisores) 509 = {509} (NUMERO PRIMO) 510 = {2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510} (15 divisores) 511 = {7, 73, 511} (3 divisores) 512 = {2, 4, 8, 16, 32, 64, 128, 256, 512} (9 divisores) 513 = {3, 9, 19, 27, 57, 171, 513} (7 divisores)
514 = {2, 257, 514} (3 divisores) 515 = {5, 103, 515} (3 divisores) 516 = {2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516} (11 divisores) 517 = {11, 47, 517} (3 divisores) 518 = {2, 7, 14, 37, 74, 259, 518} (7 divisores) 519 = {3, 173, 519} (3 divisores) 520 = {2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520} (15 divisores) 521 = {521} (NUMERO PRIMO) 522 = {2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522} (11 divisores) 523 = {523} (NUMERO PRIMO) 524 = {2, 4, 131, 262, 524} (5 divisores) 525 = {3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525} (11 divisores) 526 = {2, 263, 526} (3 divisores) 527 = {17, 31, 527} (3 divisores) 528 = {2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528} (19 divisores) 529 = {23, 529} (2 divisores) 530 = {2, 5, 10, 53, 106, 265, 530} (7 divisores) 531 = {3, 9, 59, 177, 531} (5 divisores) 532 = {2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 532} (11 divisores) 533 = {13, 41, 533} (3 divisores) 534 = {2, 3, 6, 89, 178, 267, 534} (7 divisores) 535 = {5, 107, 535} (3 divisores) 536 = {2, 4, 8, 67, 134, 268, 536} (7 divisores) 537 = {3, 179, 537} (3 divisores) 538 = {2, 269, 538} (3 divisores) 539 = {7, 11, 49, 77, 539} (5 divisores) 540 = {2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540} ( 23 divisores) 541 = {541} (NUMERO PRIMO) 542 = {2, 271, 542} (3 divisores) 543 = {3, 181, 543} (3 divisores) 544 = {2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544} (11 divisores) 545 = {5, 109, 545} (3 divisores) 546 = {2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546} (15 divisores) 547 = {547} (NUMERO PRIMO) 548 = {2, 4, 137, 274, 548} (5 divisores) 549 = {3, 9, 61, 183, 549} (5 divisores) 550 = {2, 5, 10, 11, 22, 25, 50, 55, 110, 275, 550} (11 divisores)
551 = {19, 29, 551} (3 divisores) 552 = {2, 3, 4, 6, 8, 12, 23, 24, 46, 69, 92, 138, 184, 276, 552} (15 divisores) 553 = {7, 79, 553} (3 divisores) 554 = {2, 277, 554} (3 divisores) 555 = {3, 5, 15, 37, 111, 185, 555} (7 divisores) 556 = {2, 4, 139, 278, 556} (5 divisores) 557 = {557} (NUMERO PRIMO) 558 = {2, 3, 6, 9, 18, 31, 62, 93, 186, 279, 558} (11 divisores) 559 = {13, 43, 559} (3 divisores) 560 = {2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560} (19 divisores) 561 = {3, 11, 17, 33, 51, 187, 561} (7 divisores) 562 = {2, 281, 562} (3 divisores) 563 = {563} (NUMERO PRIMO) 564 = {2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564} (11 divisores) 565 = {5, 113, 565} (3 divisores) 566 = {2, 283, 566} (3 divisores) 567 = {3, 7, 9, 21, 27, 63, 81, 189, 567} (9 divisores) 568 = {2, 4, 8, 71, 142, 284, 568} (7 divisores) 569 = {569} (NUMERO PRIMO) 570 = {2, 3, 5, 6, 10, 15, 19, 30, 38, 57, 95, 114, 190, 285, 570} (15 divisores) 571 = {571} (NUMERO PRIMO) 572 = {2, 4, 11, 13, 22, 26, 44, 52, 143, 286, 572} (11 divisores) 573 = {3, 191, 573} (3 divisores) 574 = {2, 7, 14, 41, 82, 287, 574} (7 divisores) 575 = {5, 23, 25, 115, 575} (5 divisores) 576 = {2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576} (20 divisores) 577 = {577} (NUMERO PRIMO) 578 = {2, 17, 34, 289, 578} (5 divisores) 579 = {3, 193, 579} (3 divisores) 580 = {2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580} (11 divisores) 581 = {7, 83, 581} (3 divisores) 582 = {2, 3, 6, 97, 194, 291, 582} (7 divisores) 583 = {11, 53, 583} (3 divisores) 584 = {2, 4, 8, 73, 146, 292, 584} (7 divisores) 585 = {3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585} (11 divisores) 586 = {2, 293, 586} (3 divisores) 587 = {587} (NUMERO PRIMO)
588 = {2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588} (17 divisores) 589 = {19, 31, 589} (3 divisores) 590 = {2, 5, 10, 59, 118, 295, 590} (7 divisores) 591 = {3, 197, 591} (3 divisores) 592 = {2, 4, 8, 16, 37, 74, 148, 296, 592} (9 divisores) 593 = {593} (NUMERO PRIMO) 594 = {2, 3, 6, 9, 11, 18, 22, 27, 33, 54, 66, 99, 198, 297, 594} (15 divisores) 595 = {5, 7, 17, 35, 85, 119, 595} (7 divisores) 596 = {2, 4, 149, 298, 596} (5 divisores) 597 = {3, 199, 597} (3 divisores) 598 = {2, 13, 23, 26, 46, 299, 598} (7 divisores) 599 = {599} (NUMERO PRIMO) 600 = {2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600} ( 23 divisores) 601 = {601} (NUMERO PRIMO) 602 = {2, 7, 14, 43, 86, 301, 602} (7 divisores) 603 = {3, 9, 67, 201, 603} (5 divisores) 604 = {2, 4, 151, 302, 604} (5 divisores) 605 = {5, 11, 55, 121, 605} (5 divisores) 606 = {2, 3, 6, 101, 202, 303, 606} (7 divisores) 607 = {607} (NUMERO PRIMO) 608 = {2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608} (11 divisores) 609 = {3, 7, 21, 29, 87, 203, 609} (7 divisores) 610 = {2, 5, 10, 61, 122, 305, 610} (7 divisores) 611 = {13, 47, 611} (3 divisores) 612 = {2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612} (17 divisores) 613 = {613} (NUMERO PRIMO) 614 = {2, 307, 614} (3 divisores) 615 = {3, 5, 15, 41, 123, 205, 615} (7 divisores) 616 = {2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616} (15 divisores) 617 = {617} (NUMERO PRIMO) 618 = {2, 3, 6, 103, 206, 309, 618} (7 divisores) 619 = {619} (NUMERO PRIMO) 620 = {2, 4, 5, 10, 20, 31, 62, 124, 155, 310, 620} (11 divisores) 621 = {3, 9, 23, 27, 69, 207, 621} (7 divisores) 622 = {2, 311, 622} (3 divisores) 623 = {7, 89, 623} (3 divisores)
624 = {2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624} (19 divisores) 625 = {5, 25, 125, 625} (4 divisores) 626 = {2, 313, 626} (3 divisores) 627 = {3, 11, 19, 33, 57, 209, 627} (7 divisores) 628 = {2, 4, 157, 314, 628} (5 divisores) 629 = {17, 37, 629} (3 divisores) 630 = {2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630} ( 23 divisores) 631 = {631} (NUMERO PRIMO) 632 = {2, 4, 8, 79, 158, 316, 632} (7 divisores) 633 = {3, 211, 633} (3 divisores) 634 = {2, 317, 634} (3 divisores) 635 = {5, 127, 635} (3 divisores) 636 = {2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636} (11 divisores) 637 = {7, 13, 49, 91, 637} (5 divisores) 638 = {2, 11, 22, 29, 58, 319, 638} (7 divisores) 639 = {3, 9, 71, 213, 639} (5 divisores) 640 = {2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640} (15 divisores) 641 = {641} (NUMERO PRIMO) 642 = {2, 3, 6, 107, 214, 321, 642} (7 divisores) 643 = {643} (NUMERO PRIMO) 644 = {2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644} (11 divisores) 645 = {3, 5, 15, 43, 129, 215, 645} (7 divisores) 646 = {2, 17, 19, 34, 38, 323, 646} (7 divisores) 647 = {647} (NUMERO PRIMO) 648 = {2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648} (19 divisores) 649 = {11, 59, 649} (3 divisores) 650 = {2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650} (11 divisores) 651 = {3, 7, 21, 31, 93, 217, 651} (7 divisores) 652 = {2, 4, 163, 326, 652} (5 divisores) 653 = {653} (NUMERO PRIMO) 654 = {2, 3, 6, 109, 218, 327, 654} (7 divisores) 655 = {5, 131, 655} (3 divisores) 656 = {2, 4, 8, 16, 41, 82, 164, 328, 656} (9 divisores) 657 = {3, 9, 73, 219, 657} (5 divisores) 658 = {2, 7, 14, 47, 94, 329, 658} (7 divisores) 659 = {659} (NUMERO PRIMO) 660 = {2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110,
132, 165, 220, 330, 660} ( 23 divisores) 661 = {661} (NUMERO PRIMO) 662 = {2, 331, 662} (3 divisores) 663 = {3, 13, 17, 39, 51, 221, 663} (7 divisores) 664 = {2, 4, 8, 83, 166, 332, 664} (7 divisores) 665 = {5, 7, 19, 35, 95, 133, 665} (7 divisores) 666 = {2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666} (11 divisores) 667 = {23, 29, 667} (3 divisores) 668 = {2, 4, 167, 334, 668} (5 divisores) 669 = {3, 223, 669} (3 divisores) 670 = {2, 5, 10, 67, 134, 335, 670} (7 divisores) 671 = {11, 61, 671} (3 divisores) 672 = {2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 84, 96, 112, 168, 224, 336, 672} ( 23 divisores) 673 = {673} (NUMERO PRIMO) 674 = {2, 337, 674} (3 divisores) 675 = {3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675} (11 divisores) 676 = {2, 4, 13, 26, 52, 169, 338, 676} (8 divisores) 677 = {677} (NUMERO PRIMO) 678 = {2, 3, 6, 113, 226, 339, 678} (7 divisores) 679 = {7, 97, 679} (3 divisores) 680 = {2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680} (15 divisores) 681 = {3, 227, 681} (3 divisores) 682 = {2, 11, 22, 31, 62, 341, 682} (7 divisores) 683 = {683} (NUMERO PRIMO) 684 = {2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684} (17 divisores) 685 = {5, 137, 685} (3 divisores) 686 = {2, 7, 14, 49, 98, 343, 686} (7 divisores) 687 = {3, 229, 687} (3 divisores) 688 = {2, 4, 8, 16, 43, 86, 172, 344, 688} (9 divisores) 689 = {13, 53, 689} (3 divisores) 690 = {2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690} (15 divisores) 691 = {691} (NUMERO PRIMO) 692 = {2, 4, 173, 346, 692} (5 divisores) 693 = {3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693} (11 divisores) 694 = {2, 347, 694} (3 divisores) 695 = {5, 139, 695} (3 divisores) 696 = {2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, 696} (15
divisores) 697 = {17, 41, 697} (3 divisores) 698 = {2, 349, 698} (3 divisores) 699 = {3, 233, 699} (3 divisores) 700 = {2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700} (17 divisores) 701 = {701} (NUMERO PRIMO) 702 = {2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702} (15 divisores) 703 = {19, 37, 703} (3 divisores) 704 = {2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 176, 352, 704} (13 divisores) 705 = {3, 5, 15, 47, 141, 235, 705} (7 divisores) 706 = {2, 353, 706} (3 divisores) 707 = {7, 101, 707} (3 divisores) 708 = {2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708} (11 divisores) 709 = {709} (NUMERO PRIMO) 710 = {2, 5, 10, 71, 142, 355, 710} (7 divisores) 711 = {3, 9, 79, 237, 711} (5 divisores) 712 = {2, 4, 8, 89, 178, 356, 712} (7 divisores) 713 = {23, 31, 713} (3 divisores) 714 = {2, 3, 6, 7, 14, 17, 21, 34, 42, 51, 102, 119, 238, 357, 714} (15 divisores) 715 = {5, 11, 13, 55, 65, 143, 715} (7 divisores) 716 = {2, 4, 179, 358, 716} (5 divisores) 717 = {3, 239, 717} (3 divisores) 718 = {2, 359, 718} (3 divisores) 719 = {719} (NUMERO PRIMO) 720 = {2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120 , 144, 180, 240, 360, 720} (29 divisores) 721 = {7, 103, 721} (3 divisores) 722 = {2, 19, 38, 361, 722} (5 divisores) 723 = {3, 241, 723} (3 divisores) 724 = {2, 4, 181, 362, 724} (5 divisores) 725 = {5, 25, 29, 145, 725} (5 divisores) 726 = {2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726} (11 divisores) 727 = {727} (NUMERO PRIMO) 728 = {2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728} (15 divisores) 729 = {3, 9, 27, 81, 243, 729} (6 divisores) 730 = {2, 5, 10, 73, 146, 365, 730} (7 divisores) 731 = {17, 43, 731} (3 divisores)
732 = {2, 3, 4, 6, 12, 61, 122, 183, 244, 366, 732} (11 divisores) 733 = {733} (NUMERO PRIMO) 734 = {2, 367, 734} (3 divisores) 735 = {3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735} (11 divisores) 736 = {2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736} (11 divisores) 737 = {11, 67, 737} (3 divisores) 738 = {2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738} (11 divisores) 739 = {739} (NUMERO PRIMO) 740 = {2, 4, 5, 10, 20, 37, 74, 148, 185, 370, 740} (11 divisores) 741 = {3, 13, 19, 39, 57, 247, 741} (7 divisores) 742 = {2, 7, 14, 53, 106, 371, 742} (7 divisores) 743 = {743} (NUMERO PRIMO) 744 = {2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744} (15 divisores) 745 = {5, 149, 745} (3 divisores) 746 = {2, 373, 746} (3 divisores) 747 = {3, 9, 83, 249, 747} (5 divisores) 748 = {2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748} (11 divisores) 749 = {7, 107, 749} (3 divisores) 750 = {2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750} (15 divisores) 751 = {751} (NUMERO PRIMO) 752 = {2, 4, 8, 16, 47, 94, 188, 376, 752} (9 divisores) 753 = {3, 251, 753} (3 divisores) 754 = {2, 13, 26, 29, 58, 377, 754} (7 divisores) 755 = {5, 151, 755} (3 divisores) 756 = {2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378, 756} ( 23 divisores) 757 = {757} (NUMERO PRIMO) 758 = {2, 379, 758} (3 divisores) 759 = {3, 11, 23, 33, 69, 253, 759} (7 divisores) 760 = {2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760} (15 divisores) 761 = {761} (NUMERO PRIMO) 762 = {2, 3, 6, 127, 254, 381, 762} (7 divisores) 763 = {7, 109, 763} (3 divisores) 764 = {2, 4, 191, 382, 764} (5 divisores) 765 = {3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765} (11 divisores) 766 = {2, 383, 766} (3 divisores) 767 = {13, 59, 767} (3 divisores) 768 = {2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768}
(17 divisores) 769 = {769} (NUMERO PRIMO) 770 = {2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770} (15 divisores) 771 = {3, 257, 771} (3 divisores) 772 = {2, 4, 193, 386, 772} (5 divisores) 773 = {773} (NUMERO PRIMO) 774 = {2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774} (11 divisores) 775 = {5, 25, 31, 155, 775} (5 divisores) 776 = {2, 4, 8, 97, 194, 388, 776} (7 divisores) 777 = {3, 7, 21, 37, 111, 259, 777} (7 divisores) 778 = {2, 389, 778} (3 divisores) 779 = {19, 41, 779} (3 divisores) 780 = {2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780} ( 23 divisores) 781 = {11, 71, 781} (3 divisores) 782 = {2, 17, 23, 34, 46, 391, 782} (7 divisores) 783 = {3, 9, 27, 29, 87, 261, 783} (7 divisores) 784 = {2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784} (14 divisores) 785 = {5, 157, 785} (3 divisores) 786 = {2, 3, 6, 131, 262, 393, 786} (7 divisores) 787 = {787} (NUMERO PRIMO) 788 = {2, 4, 197, 394, 788} (5 divisores) 789 = {3, 263, 789} (3 divisores) 790 = {2, 5, 10, 79, 158, 395, 790} (7 divisores) 791 = {7, 113, 791} (3 divisores) 792 = {2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 132, 198, 264, 396, 792} ( 23 divisores) 793 = {13, 61, 793} (3 divisores) 794 = {2, 397, 794} (3 divisores) 795 = {3, 5, 15, 53, 159, 265, 795} (7 divisores) 796 = {2, 4, 199, 398, 796} (5 divisores) 797 = {797} (NUMERO PRIMO) 798 = {2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399, 798} (15 divisores) 799 = {17, 47, 799} (3 divisores) 800 = {2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800} (17 divisores) 801 = {3, 9, 89, 267, 801} (5 divisores) 802 = {2, 401, 802} (3 divisores)
803 = {11, 73, 803} (3 divisores) 804 = {2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804} (11 divisores) 805 = {5, 7, 23, 35, 115, 161, 805} (7 divisores) 806 = {2, 13, 26, 31, 62, 403, 806} (7 divisores) 807 = {3, 269, 807} (3 divisores) 808 = {2, 4, 8, 101, 202, 404, 808} (7 divisores) 809 = {809} (NUMERO PRIMO) 810 = {2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810} (19 divisores) 811 = {811} (NUMERO PRIMO) 812 = {2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812} (11 divisores) 813 = {3, 271, 813} (3 divisores) 814 = {2, 11, 22, 37, 74, 407, 814} (7 divisores) 815 = {5, 163, 815} (3 divisores) 816 = {2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816} (19 divisores) 817 = {19, 43, 817} (3 divisores) 818 = {2, 409, 818} (3 divisores) 819 = {3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819} (11 divisores) 820 = {2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820} (11 divisores) 821 = {821} (NUMERO PRIMO) 822 = {2, 3, 6, 137, 274, 411, 822} (7 divisores) 823 = {823} (NUMERO PRIMO) 824 = {2, 4, 8, 103, 206, 412, 824} (7 divisores) 825 = {3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825} (11 divisores) 826 = {2, 7, 14, 59, 118, 413, 826} (7 divisores) 827 = {827} (NUMERO PRIMO) 828 = {2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828} (17 divisores) 829 = {829} (NUMERO PRIMO) 830 = {2, 5, 10, 83, 166, 415, 830} (7 divisores) 831 = {3, 277, 831} (3 divisores) 832 = {2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832} (13 divisores) 833 = {7, 17, 49, 119, 833} (5 divisores) 834 = {2, 3, 6, 139, 278, 417, 834} (7 divisores) 835 = {5, 167, 835} (3 divisores) 836 = {2, 4, 11, 19, 22, 38, 44, 76, 209, 418, 836} (11 divisores) 837 = {3, 9, 27, 31, 93, 279, 837} (7 divisores) 838 = {2, 419, 838} (3 divisores) 839 = {839} (NUMERO PRIMO) 840 = {2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56,
60, 70, 84, 105 , 120, 140, 168, 210, 280, 420, 840} (31 divisores) 841 = {29, 841} (2 divisores) 842 = {2, 421, 842} (3 divisores) 843 = {3, 281, 843} (3 divisores) 844 = {2, 4, 211, 422, 844} (5 divisores) 845 = {5, 13, 65, 169, 845} (5 divisores) 846 = {2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846} (11 divisores) 847 = {7, 11, 77, 121, 847} (5 divisores) 848 = {2, 4, 8, 16, 53, 106, 212, 424, 848} (9 divisores) 849 = {3, 283, 849} (3 divisores) 850 = {2, 5, 10, 17, 25, 34, 50, 85, 170, 425, 850} (11 divisores) 851 = {23, 37, 851} (3 divisores) 852 = {2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852} (11 divisores) 853 = {853} (NUMERO PRIMO) 854 = {2, 7, 14, 61, 122, 427, 854} (7 divisores) 855 = {3, 5, 9, 15, 19, 45, 57, 95, 171, 285, 855} (11 divisores) 856 = {2, 4, 8, 107, 214, 428, 856} (7 divisores) 857 = {857} (NUMERO PRIMO) 858 = {2, 3, 6, 11, 13, 22, 26, 33, 39, 66, 78, 143, 286, 429, 858} (15 divisores) 859 = {859} (NUMERO PRIMO) 860 = {2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860} (11 divisores) 861 = {3, 7, 21, 41, 123, 287, 861} (7 divisores) 862 = {2, 431, 862} (3 divisores) 863 = {863} (NUMERO PRIMO) 864 = {2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864} ( 23 divisores) 865 = {5, 173, 865} (3 divisores) 866 = {2, 433, 866} (3 divisores) 867 = {3, 17, 51, 289, 867} (5 divisores) 868 = {2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868} (11 divisores) 869 = {11, 79, 869} (3 divisores) 870 = {2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870} (15 divisores) 871 = {13, 67, 871} (3 divisores) 872 = {2, 4, 8, 109, 218, 436, 872} (7 divisores) 873 = {3, 9, 97, 291, 873} (5 divisores) 874 = {2, 19, 23, 38, 46, 437, 874} (7 divisores) 875 = {5, 7, 25, 35, 125, 175, 875} (7 divisores) 876 = {2, 3, 4, 6, 12, 73, 146, 219, 292, 438, 876} (11 divisores) 877 = {877} (NUMERO PRIMO)
878 = {2, 439, 878} (3 divisores) 879 = {3, 293, 879} (3 divisores) 880 = {2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 176, 220, 440, 880} (19 divisores) 881 = {881} (NUMERO PRIMO) 882 = {2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882} (17 divisores) 883 = {883} (NUMERO PRIMO) 884 = {2, 4, 13, 17, 26, 34, 52, 68, 221, 442, 884} (11 divisores) 885 = {3, 5, 15, 59, 177, 295, 885} (7 divisores) 886 = {2, 443, 886} (3 divisores) 887 = {887} (NUMERO PRIMO) 888 = {2, 3, 4, 6, 8, 12, 24, 37, 74, 111, 148, 222, 296, 444, 888} (15 divisores) 889 = {7, 127, 889} (3 divisores) 890 = {2, 5, 10, 89, 178, 445, 890} (7 divisores) 891 = {3, 9, 11, 27, 33, 81, 99, 297, 891} (9 divisores) 892 = {2, 4, 223, 446, 892} (5 divisores) 893 = {19, 47, 893} (3 divisores) 894 = {2, 3, 6, 149, 298, 447, 894} (7 divisores) 895 = {5, 179, 895} (3 divisores) 896 = {2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 112, 128, 224, 448, 896} (15 divisores) 897 = {3, 13, 23, 39, 69, 299, 897} (7 divisores) 898 = {2, 449, 898} (3 divisores) 899 = {29, 31, 899} (3 divisores) 900 = {2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300 , 450, 900} (26 divisores) 901 = {17, 53, 901} (3 divisores) 902 = {2, 11, 22, 41, 82, 451, 902} (7 divisores) 903 = {3, 7, 21, 43, 129, 301, 903} (7 divisores) 904 = {2, 4, 8, 113, 226, 452, 904} (7 divisores) 905 = {5, 181, 905} (3 divisores) 906 = {2, 3, 6, 151, 302, 453, 906} (7 divisores) 907 = {907} (NUMERO PRIMO) 908 = {2, 4, 227, 454, 908} (5 divisores) 909 = {3, 9, 101, 303, 909} (5 divisores) 910 = {2, 5, 7, 10, 13, 14, 26, 35, 65, 70, 91, 130, 182, 455, 910} (15 divisores) 911 = {911} (NUMERO PRIMO) 912 = {2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304,
456, 912}(19 divisores) 913 = {11, 83, 913}(3 divisores) 914 = {2, 457, 914}(3 divisores) 915 = {3, 5, 15, 61, 183, 305, 915}(7 divisores) 916 = {2, 4, 229, 458, 916}(5 divisores) 917 = {7, 131, 917}(3 divisores) 918 = {2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459, 918}(15 divisores) 919 = {919} (NUMERO PRIMO) 920 = {2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920}(15 divisores) 921 = {3, 307, 921}(3 divisores) 922 = {2, 461, 922}(3 divisores) 923 = {13, 71, 923}(3 divisores) 924 = {2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924}(23 divisores) 925 = {5, 25, 37, 185, 925}(5 divisores) 926 = {2, 463, 926}(3 divisores) 927 = {3, 9, 103, 309, 927}(5 divisores) 928 = {2, 4, 8, 16, 29, 32, 58, 116, 232, 464, 928}(11 divisores) 929 = {929} (NUMERO PRIMO) 930 = {2, 3, 5, 6, 10, 15, 30, 31, 62, 93, 155, 186, 310, 465, 930}(15 divisores) 931 = {7, 19, 49, 133, 931}(5 divisores) 932 = {2, 4, 233, 466, 932}(5 divisores) 933 = {3, 311, 933}(3 divisores) 934 = {2, 467, 934}(3 divisores) 935 = {5, 11, 17, 55, 85, 187, 935}(7 divisores) 936 = {2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 72, 78, 104, 117, 156, 234, 312, 468, 936}(23 divisores) 937 = {937} (NUMERO PRIMO) 938 = {2, 7, 14, 67, 134, 469, 938}(7 divisores) 939 = {3, 313, 939}(3 divisores) 940 = {2, 4, 5, 10, 20, 47, 94, 188, 235, 470, 940}(11 divisores) 941 = {941} (NUMERO PRIMO) 942 = {2, 3, 6, 157, 314, 471, 942}(7 divisores) 943 = {23, 41, 943}(3 divisores) 944 = {2, 4, 8, 16, 59, 118, 236, 472, 944}(9 divisores) 945 = {3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945}(15 divisores) 946 = {2, 11, 22, 43, 86, 473, 946}(7 divisores)
947 = {947} (NUMERO PRIMO) 948 = {2, 3, 4, 6, 12, 79, 158, 237, 316, 474, 948}(11 divisores) 949 = {13, 73, 949}(3 divisores) 950 = {2, 5, 10, 19, 25, 38, 50, 95, 190, 475, 950}(11 divisores) 951 = {3, 317, 951}(3 divisores) 952 = {2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476, 952}(15 divisores) 953 = {953} (NUMERO PRIMO) 954 = {2, 3, 6, 9, 18, 53, 106, 159, 318, 477, 954}(11 divisores) 955 = {5, 191, 955}(3 divisores) 956 = {2, 4, 239, 478, 956}(5 divisores) 957 = {3, 11, 29, 33, 87, 319, 957}(7 divisores) 958 = {2, 479, 958}(3 divisores) 959 = {7, 137, 959}(3 divisores) 960 = {2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960}(27 divisores) 961 = {31, 961}(2 divisores) 962 = {2, 13, 26, 37, 74, 481, 962}(7 divisores) 963 = {3, 9, 107, 321, 963}(5 divisores) 964 = {2, 4, 241, 482, 964}(5 divisores) 965 = {5, 193, 965}(3 divisores) 966 = {2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966}(15 divisores) 967 = {967} (NUMERO PRIMO) 968 = {2, 4, 8, 11, 22, 44, 88, 121, 242, 484, 968}(11 divisores) 969 = {3, 17, 19, 51, 57, 323, 969}(7 divisores) 970 = {2, 5, 10, 97, 194, 485, 970}(7 divisores) 971 = {971} (NUMERO PRIMO) 972 = {2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972} (17 divisores) 973 = {7, 139, 973}(3 divisores) 974 = {2, 487, 974}(3 divisores) 975 = {3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975}(11 divisores) 976 = {2, 4, 8, 16, 61, 122, 244, 488, 976}(9 divisores) 977 = {977} (NUMERO PRIMO) 978 = {2, 3, 6, 163, 326, 489, 978}(7 divisores) 979 = {11, 89, 979}(3 divisores) 980 = {2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980} (17 divisores) 981 = {3, 9, 109, 327, 981}(5 divisores) 982 = {2, 491, 982}(3 divisores)
983 = {983} (NUMERO PRIMO) 984 = {2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984}(15 divisores) 985 = {5, 197, 985}(3 divisores) 986 = {2, 17, 29, 34, 58, 493, 986}(7 divisores) 987 = {3, 7, 21, 47, 141, 329, 987}(7 divisores) 988 = {2, 4, 13, 19, 26, 38, 52, 76, 247, 494, 988}(11 divisores) 989 = {23, 43, 989}(3 divisores) 990 = {2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990}(23 divisores) 991 = {991} (NUMERO PRIMO) 992 = {2, 4, 8, 16, 31, 32, 62, 124, 248, 496, 992}(11 divisores) 993 = {3, 331, 993}(3 divisores) 994 = {2, 7, 14, 71, 142, 497, 994}(7 divisores) 995 = {5, 199, 995}(3 divisores) 996 = {2, 3, 4, 6, 12, 83, 166, 249, 332, 498, 996}(11 divisores) 997 = {997} (NUMERO PRIMO) 998 = {2, 499, 998}(3 divisores) 999 = {3, 9, 27, 37, 111, 333, 999}(7 divisores) 1000 = {2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000}(15 divisores)
Criba de Aschero La Criba de Aschero presenta un modelo que parte de un principio distinto, obteniendo el mismo resultado pero con un procedimiento mucho ms simplificado que el de Eratstenes para descubrir en este caso los 168 nmeros primos dentro de los primeros 1000 nmeros naturales. Veamos como:
Empezamos por escribir una cruz numeral con los tres primeros nmeros impares dejando el 1 y el 5 como inicio y el 3 como centro (nmero primo que junto al 2 quedan separados de la operatoria).
1 1 3 5 5
A continuacin sumamos el nmero superior con los dos laterales centrales: 1 + 1 + 5 = 7 obteniendo un resultado.
Hacemos lo mismo con el nmero inferior sumado a los dos laterales centrales: 5 + 1 + 5 = 11. El resultado de estos dos primeros trinomios es:
1 =7 1 3 5 5 = 11
A esto se le agrega una segunda cruz que se inicia con el nmero central de la anterior:
3 3 5 7 7 = 17
= 13
Y as se van obteniendo dos resultados por cada cruz que sucesivamente generan una serie numrica de dos niveles de lectura. La separacin entre el nmero superior y el inferior es siempre cuatro y la de cada binomio (en orden), dos.7 11 103 107 13 17 109 113 19 23 115 119 25 29 121 125 31 35 127 131 37 41 133 137 43 47 139 143 49 53 145 149 55 59 151 155 61 65 157 161 67 71 163 167 73 77 169 173 79 83 175 179 85 89 181 185 91 95 187 191
1 5 97 101
193 197
199 203
205 209
211 215
217 221
223 227
229 233
235 239
241 245
247 251
253 257
259 263
265 269
271 275
277 281
283 287
289 293
295 299
301 305
307 311
313 317
319 323
325 329
331 335
337 341
343 347
349 353
355 359
361 365
367 371
373 377
379 383
385 389
391 395
397 401
403 407
409 413
415 419
421 425
427 431
433 437
439 443
445 449
451 455
457 461
463 467
469 473
475 479
481 485
487 491
493 497
499 503
505 509
511 515
517 521
523 527
529 533
535 539
541 545
547 551
553 557
559 563
565 569
571 575
577 581
583 587
589 593
595 599
601 605
607 611
613 617
619 623
625 629
631 635
637 641
643 647
649 653
655 659
661 665
667 671
673 677
679 683
685 689
691 695
697 701
703 707
709 713
715 719
721 725
727 731
733 737
739 743
745 749
751 755
757 761
763 767
769 773
775 779
781 785
787 791
793 797
799 803
805 809
811 815
817 821
823 827
829 833
835 839
841 845
847 851
853 857
859 863
865 869 961 965
871 875 967 971
877 881 973 977
883 887 979 983
889 893 985 989
895 899 991 995
901 905 997
907 911
913 917
919 923
925 929
931 935
937 941
943 947
949 953
955 959
En la Criba de Aschero hay 333 nmeros impares (en lugar de los 1000 de la Criba de Eratstenes). Procedimiento para cribar los nmeros compuestos.
A) El modelo a seguir es el fijado por la secuencia numeral establecida: 5, 7, 11, 13, 17, 19, 23, 25, 29 y 31 B) Partiendo de dos primeras multiplicaciones: 5 x 5 = 25 (lnea superior) y 5 x 7 = 35 (lnea inferior), obtenemos dos resultados que significan el punto de partida de la primera criba. Todos los nmeros que se encuentran a un intervalo de cinco (5) casilleros del resultado de cada una de las dos multiplicaciones, deben ser coloreados de rojo ya que no son primos.
1 5 97 101
7 11 103 107
13 17 109 113
19 23 115 119
25 29 121 125
31 35 127 131
37 41 133 137
43 47 139 143
49 53 145 149
55 59 151 155
61 65 157 161
67 71 163 167
73 77 169 173
79 83 175 179
85 89 181 185
91 95 187 191
193 197
199 203
205 209
211 215
217 221
223 227
229 233
235 239
241 245
247 251
253 257
259 263
265 269
271 275
277 281
283 287
289 293
295 299
301 305
307 311
313 317
319 323
325 329
331 335
337 341
343 347
349 353
355 359
361 365
367 371
373 377
379 383
385 389
391 395
397 401
403 407
409 413
415 419
421 425
427 431
433 437
439 443
445 449
451 455
457 461
463 467
469 473
475 479
481 485
487 491
493 497
499 503
505 509
511 515
517 521
523 527
529 533
535 539
541 545
547 551
553 557
559 563
565 569
571 575
577 581
583 587
589 593
595 599
601 605
607 611
613 617
619 623
625 629
631 635
637 641
643 647
649 653
655 659
661 665
667 671
673 677
679 683
685 689
691 695
697 701
703 707
709 713
715 719
721 725
727 731
733 737
739 743
745 749
751 755
757 761
763 767
769 773
775 779
781 785
787 791
793 797
799 803
805 809
811 815
817 821
823 827
829 833
835 839
841 845
847 851
853 857
859 863
865 869 961 965
871 875 967 971
877 881 973 977
883 887 979 983
889 893 985 989
895 899 991 995
901 905 997
907 911
913 917
919 923
925 929
931 935
937 941
943 947
949 953
955 959
C) Se sigue con las multiplicaciones: 7 x 7 = 49 (lnea superior) y 7 x 11 = 77 (lnea inferior), con lo que obtenemos dos resultados que significan el punto de partida de una segunda criba. Todos los nmeros que se encuentran a un intervalo de siete (7) casilleros del resultado de cada una de las dos multiplicaciones, deben ser coloreados de rojo ya que no son primos.
D) Se produce superposicin en el borrado de los siguientes nmeros: 245 (5 y 7) 385 (5 y 7) 455 (5 y 7) 595 (5 y 7) 665 (5 y 7) 805 (5 y 7) 875 (5 y 7)
1 5 97 101
7 11 103 107
13 17 109 113
19 23 115 119
25 29 121 125
31 35 127 131
37 41 133 137
43 47 139 143
49 53 145 149
55 59 151 155
61 65 157 161
67 71 163 167
73 77 169 173
79 83 175 179
85 89 181 185
91 95 187 191
193 197
199 203
205 209
211 215
217 221
223 227
229 233
235 239
241 245
247 251
253 257
259 263
265 269
271 275
277 281
283 287
289 293
295 299
301 305
307 311
313 317
319 323
325 329
331 335
337 341
343 347
349 353
355 359
361 365
367 371
373 377
379 383
385 389
391 395
397 401
403 407
409 413
415 419
421 425
427 431
433 437
439 443
445 449
451 455
457 461
463 467
469 473
475 479
481 485
487 491
493 497
499 503
505 509
511 515
517 521
523 527
529 533
535 539
541 545
547 551
553 557
559 563
565 569
571 575
577 581
583 587
589 593
595 599
601 605
607 611
613 617
619 623
625 629
631 635
637 641
643 647
649 653
655 659
661 665
667 671
673 677
679 683
685 689
691 695
697 701
703 707
709 713
715 719
721 725
727 731
733 737
739 743
745 749
751 755
757 761
763 767
769 773
775 779
781 785
787 791
793 797
799 803
805 809
811 815
817 821
823 827
829 833
835 839
841 845
847 851
853 857
859 863
865 869 961 965
871 875 967 971
877 881 973 977
883 887 979 983
889 893 985 989
895 899 991 995
901 905 997
907 911
913 917
919 923
925 929
931 935
937 941
943 947
949 953
955 959
E) Se sigue con las multiplicaciones: 11 x 11 = 121 (lnea superior) y 11 x 13 = 143 (lnea inferior), con lo que obtenemos dos resultados que significan el punto de partida de una tercera criba. Todos los nmeros que se encuentran a un intervalo de once (11) casilleros del resultado de cada una de las dos multiplicaciones, deben ser coloreados de rojo ya que no son primos.
F) Se produce superposicin en el borrado de los siguientes nmeros: 275 (5 y 11) 385 (5, 7 y 11) 539 (7 y 11) 605 (5 y 11) 715 (5 y 11) 847 (7 y 11) 935 (5 y 11)
1 5 97 101
7 11 103 107
13 17 109 113
19 23 115 119
25 29 121 125
31 35 127 131
37 41 133 137
43 47 139 143
49 53 145 149
55 59 151 155
61 65 157 161
67 71 163 167
73 77 169 173
79 83 175 179
85 89 181 185
91 95 187 191
193 197
199 203
205 209
211 215
217 221
223 227
229 233
235 239
241 245
247 251
253 257
259 263
265 269
271 275
277 281
283 287
289 293
295 299
301 305
307 311
313 317
319 323
325 329
331 335
337 341
343 347
349 353
355 359
361 365
367 371
373 377
379 383
385 389
391 395
397 401
403 407
409 413
415 419
421 425
427 431
433 437
439 443
445 449
451 455
457 461
463 467
469 473
475 479
481 485
487 491
493 497
499 503
505 509
511 515
517 521
523 527
529 533
535 539
541 545
547 551
553 557
559 563
565 569
571 575
577 581
583 587
589 593
595 599
601 605
607 611
613 617
619 623
625 629
631 635
637 641
643 647
649 653
655 659
661 665
667 671
673 677
679 683
685 689
691 695
697 701
703 707
709 713
715 719
721 725
727 731
733 737
739 743
745 749
751 755
757 761
763 767
769 773
775 779
781 785
787 791
793 797
799 803
805 809
811 815
817 821
823 827
829 833
835 839
841 845
847 851
853 857
859 863
865 869 961 965
871 875 967 971
877 881 973 977
883 887 979 983
889 893 985 989
895 899 991 995
901 905 997
907 911
913 917
919 923
925 929
931 935
937 941
943 947
949 953
955 959
G) Se sigue con las multiplicaciones: 13 x 13 = 169 (lnea superior) y 13 x 17 = 221 (lnea inferior), con lo que obtenemos dos resultados que significan el punto de partida de una cuarta criba. Todos los nmeros que se encuentran a un intervalo de trece (13) casilleros del resultado de cada una de las dos multiplicaciones, deben ser coloreados de rojo ya que no son primos.
H) Se produce superposicin en el borrado de los siguientes nmeros: 325 (5 y 13) 455 (5, 7 y 13) 637 (7 y 13) 715 (5, 11 y 13) 845 (5 y 13)
1 5 97 101
7 11 103 107
13 17 109 113
19 23 115 119
25 29 121 125
31 35 127 131
37 41 133 137
43 47 139 143
49 53 145 149
55 59 151 155
61 65 157 161
67 71 163 167
73 77 169 173
79 83 175 179
85 89 181 185
91 95 187 191
193 197
199 203
205 209
211 215
217 221
223 227
229 233
235 239
241 245
247 251
253 257
259 263
265 269
271 275
277 281
283 287
289 293
295 299
301 305
307 311
313 317
319 323
325 329
331 335
337 341
343 347
349 353
355 359
361 365
367 371
373 377
379 383
385 389
391 395
397 401
403 407
409 413
415 419
421 425
427 431
433 437
439 443
445 449
451 455
457 461
463 467
469 473
475 479
481 485
487 491
493 497
499 503
505 509
511 515
517 521
523 527
529 533
535 539
541 545
547 551
553 557
559 563
565 569
571 575
577 581
583 587
589 593
595 599
601 605
607 611
613 617
619 623
625 629
631 635
637 641
643 647
649 653
655 659
661 665
667 671
673 677
679 683
685 689
691 695
697 701
703 707
709 713
715 719
721 725
727 731
733 737
739 743
745 749
751 755
757 761
763 767
769 773
775 779
781 785
787 791
793 797
799 803
805 809
811 815
817 821
823 827
829 833
835 839
841 845
847 851
853 857
859 863
865 869 961 965
871 875 967 971
877 881 973 977
883 887 979 983
889 893 985 989
895 899 991 995
901 905 997
907 911
913 917
919 923
925 929
931 935
937 941
943 947
949 953
955 959
I) Se sigue con las multiplicaciones: 17 x 17 = 289 (lnea superior) y 17 x 19 = 221 (lnea inferior), con lo que obtenemos dos resultados que significan el punto de partida de una quinta criba. Todos los nmeros que se encuentran a un intervalo de diecisiete (17) casilleros del resultado de cada una de las dos multiplicaciones, deben ser coloreados de rojo ya que no son primos.
J) Se produce superposicin en el borrado de los siguientes nmeros: 425 (5 y 17) 595 (5, 7 y 17) 833 (7 y 17) 935 (5, 11 y 17)
1 5 97 101
7 11 103 107
13 17 109 113
19 23 115 119
25 29 121 125
31 35 127 131
37 41 133 137
43 47 139 143
49 53 145 149
55 59 151 155
61 65 157 161
67 71 163 167
73 77 169 173
79 83 175 179
85 89 181 185
91 95 187 191
193 197
199 203
205 209
211 215
217 221
223 227
229 233
235 239
241 245
247 251
253 257
259 263
265 269
271 275
277 281
283 287
289 293
295 299
301 305
307 311
313 317
319 323
325 329
331 335
337 341
343 347
349 353
355 359
361 365
367 371
373 377
379 383
385 389
391 395
397 401
403 407
409 413
415 419
421 425
427 431
433 437
439 443
445 449
451 455
457 461
463 467
469 473
475 479
481 485
487 491
493 497
499 503
505 509
511 515
517 521
523 527
529 533
535 539
541 545
547 551
553 557
559 563
565 569
571 575
577 581
583 587
589 593
595 599
601 605
607 611
613 617
619 623
625 629
631 635
637 641
643 647
649 653
655 659
661 665
667 671
673 677
679 683
685 689
691 695
697 701
703 707
709 713
715 719
721 725
727 731
733 737
739 743
745 749
751 755
757 761
763 767
769 773
775 779
781 785
787 791
793 797
799 803
805 809
811 815
817 821
823 827
829 833
835 839
841 845
847 851
853 857
859 863
865 869 961 965
871 875 967 971
877 881 973 977
883 887 979 983
889 893 985 989
895 899 991 995
901 905 997
907 911
913 917
919 923
925 929
931 935
937 941
943 947
949 953
955 959
K) Se sigue con las multiplicaciones: 19 x 19 = 361 (lnea superior) y 19 x 23 = 437 (lnea inferior), con lo que obtenemos dos resultados que significan el punto de partida de una sexta criba. Todos los nmeros que se encuentran a un intervalo de diecinueve (19) casilleros del resultado de cada una de las dos multiplicaciones, deben ser coloreados de rojo ya que no son primos.
L) Se produce superposicin en el borrado de los siguientes nmeros: 475 (5 y 19) 665 (5, 7 y 19) 931 (7 y 19)
1 5 97 101
7 11 103 107
13 17 109 113
19 23 115 119
25 29 121 125
31 35 127 131
37 41 133 137
43 47 139 143
49 53 145 149
55 59 151 155
61 65 157 161
67 71 163 167
73 77 169 173
79 83 175 179
85 89 181 185
91 95 187 191
193 197
199 203
205 209
211 215
217 221
223 227
229 233
235 239
241 245
247 251
253 257
259 263
265 269
271 275
277 281
283 287
289 293
295 299
301 305
307 311
313 317
319 323
325 329
331 335
337 341
343 347
349 353
355 359
361 365
367 371
373 377
379 383
385 389
391 395
397 401
403 407
409 413
415 419
421 425
427 431
433 437
439 443
445 449
451 455
457 461
463 467
469 473
475 479
481 485
487 491
493 497
499 503
505 509
511 515
517 521
523 527
529 533
535 539
541 545
547 551
553 557
559 563
565 569
571 575
577 581
583 587
589 593
595 599
601 605
607 611
613 617
619 623
625 629
631 635
637 641
643 647
649 653
655 659
661 665
667 671
673 677
679 683
685 689
691 695
697 701
703 707
709 713
715 719
721 725
727 731
733 737
739 743
745 749
751 755
757 761
763 767
769 773
775 779
781 785
787 791
793 797
799 803
805 809
811 815
817 821
823 827
829 833
835 839
841 845
847 851
853 857
859 863
865 869 961 965
871 875 967 971
877 881 973 977
883 887 979 983
889 893 985 989
895 899 991 995
901 905 997
907 911
913 917
919 923
925 929
931 935
937 941
943 947
949 953
955 959
M) Se sigue con las multiplicaciones: 23 x 23 = 529 (lnea superior) y 23 x 25 = 575 (lnea inferior), con lo que obtenemos dos resultados que significan el punto de partida de una sptima criba. Todos los nmeros que se encuentran a un intervalo de veintitrs (23) casilleros del resultado de cada una de las dos multiplicaciones, deben ser coloreados de rojo ya que no son primos.
N) Se produce superposicin en el borrado de los siguientes nmeros: 575 (5 y 23) 805 (5, 7 y 23)
1 5 97 101
7 11 103 107
13 17 109 113
19 23 115 119
25 29 121 125
31 35 127 131
37 41 133 137
43 47 139 143
49 53 145 149
55 59 151 155
61 65 157 161
67 71 163 167
73 77 169 173
79 83 175 179
85 89 181 185
91 95 187 191
193 197
199 203
205 209
211 215
217 221
223 227
229 233
235 239
241 245
247 251
253 257
259 263
265 269
271 275
277 281
283 287
289 293
295 299
301 305
307 311
313 317
319 323
325 329
331 335
337 341
343 347
349 353
355 359
361 365
367 371
373 377
379 383
385 389
391 395
397 401
403 407
409 413
415 419
421 425
427 431
433 437
439 443
445 449
451 455
457 461
463 467
469 473
475 479
481 485
487 491
493 497
499 503
505 509
511 515
517 521
523 527
529 533
535 539
541 545
547 551
553 557
559 563
565 569
571 575
577 581
583 587
589 593
595 599
601 605
607 611
613 617
619 623
625 629
631 635
637 641
643 647
649 653
655 659
661 665
667 671
673 677
679 683
685 689
691 695
697 701
703 707
709 713
715 719
721 725
727 731
733 737
739 743
745 749
751 755
757 761
763 767
769 773
775 779
781 785
787 791
793 797
799 803
805 809
811 815
817 821
823 827
829 833
835 839
841 845
847 851
853 857
859 863
865 869 961 965
871 875 967 971
877 881 973 977
883 887 979 983
889 893 985 989
895 899 991 995
901 905 997
907 911
913 917
919 923
925 929
931 935
937 941
943 947
949 953
955 959
O) Se sigue con las multiplicaciones: 29 x 29 = 841(lnea superior) y 29 x 31 = 899 (lnea inferior), con lo que obtenemos slo dos resultados de nmeros compuestos en la octava criba.
1 5 97 101
7 11 103 107
13 17 109 113
19 23 115 119
25 29 121 125
31 35 127 131
37 41 133 137
43 47 139 143
49 53 145 149
55 59 151 155
61 65 157 161
67 71 163 167
73 77 169 173
79 83 175 179
85 89 181 185
91 95 187 191
193 197
199 203
205 209
211 215
217 221
223 227
229 233
235 239
241 245
247 251
253 257
259 263
265 269
271 275
277 281
283 287
289 293
295 299
301 305
307 311
313 317
319 323
325 329
331 335
337 341
343 347
349 353
355 359
361 365
367 371
373 377
379 383
385 389
391 395
397 401
403 407
409 413
415 419
421 425
427 431
433 437
439 443
445 449
451 455
457 461
463 467
469 473
475 479
481 485
487 491
493 497
499 503
505 509
511 515
517 521
523 527
529 533
535 539
541 545
547 551
553 557
559 563
565 569
571 575
577 581
583 587
589 593
595 599
601 605
607 611
613 617
619 623
625 629
631 635
637 641
643 647
649 653
655 659
661 665
667 671
673 677
679 683
685 689
691 695
697 701
703 707
709 713
715 719
721 725
727 731
733 737
739 743
745 749
751 755
757 761
763 767
769 773
775 779
781 785
787 791
793 797
799 803
805 809
811 815
817 821
823 827
829 833
835 839
841 845
847 851
853 857
859 863
865 869 961 965
871 875 967 971
877 881 973 977
883 887 979 983
889 893 985 989
895 899 991 995
901 905 997
907 911
913 917
919 923
925 929
931 935
937 941
943 947
949 953
955 959
P) La ltima multiplicacin y novena criba es de: 31 x 31= 961(lnea superior) y con esto finaliza este anlisis de la Criba de Aschero.
(El nmero 1 no se considera primo y el 2 y 3 quedan exceptuados de esta Criba)1 5 97 101 7 11 103 107 13 17 109 113 19 23 115 119 25 29 121 125 31 35 127 131 37 41 133 137 43 47 139 143 49 53 145 149 55 59 151 155 61 65 157 161 67 71 163 167 73 77 169 173 79 83 175 179 85 89 181 185 91 95 187 191
193 197
199 203
205 209
211 215
217 221
223 227
229 233
235 239
241 245
247 251
253 257
259 263
265 269
271 275
277 281
283 287
289 293
295 299
301 305
307 311
313 317
319 323
325 329
331 335
337 341
343 347
349 353
355 359
361 365
367 371
373 377
379 383
385 389
391 395
397 401
403 407
409 413
415 419
421 425
427 431
433 437
439 443
445 449
451 455
457 461
463 467
469 473
475 479
481 485
487 491
493 497
499 503
505 509
511 515
517 521
523 527
529 533
535 539
541 545
547 551
553 557
559 563
565 569
571 575
577 581
583 587
589 593
595 599
601 605
607 611
613 617
619 623
625 629
631 635
637 641
643 647
649 653
655 659
661 665
667 671
673 677
679 683
685 689
691 695
697 701
703 707
709 713
715 719
721 725
727 731
733 737
739 743
745 749
751 755
757 761
763 767
769 773
775 779
781 785
787 791
793 797
799 803
805 809
811 815
817 821
823 827
829 833
835 839
841 845
847 851
853 857
859 863
865 869 961 965
871 875 967 971
877 881 973 977
883 887 979 983
889 893 985 989
895 899 991 995
901 905 997
907 911
913 917
919 923
925 929
931 935
937 941
943 947
949 953
955 959
Color amarillo: nmeros primos (168)
Color rojo: nmeros compuestos (165)
Conclusin Con esto se finaliza esta muestra aritmtica con el resultado de que para analizar los nmeros primos comprendidos dentro de los1000 primeros nmeros naturales, se parte de 333 nmeros que al cribarse se sintetizan en 168 nmeros primos y 165 nmeros compuestos.
Este modelo matemtico simplifica el propuesto por Eratstenes por contener menos operadores y mayor simplicidad en su resolucin. Y tal como la Criba de Eratstenes, la Criba de Aschero es aplicable a todos los nmeros primos conocidos y por conocer.
(Para Fejga Sosnina por todo lo que me ha dado)
Buenos Aires, Argentina, 2010
Sergio Aschero (Doctor en Musicologa) [email protected] Avenida Roca 1669 (1870) Avellaneda / Provincia de Buenos Aires / Argentina http://www.ascheropus.com
