=============================================================================== Date: Thu, 04 Jul 1996 14:24:01 +0100 From: kamran.kordi@gecm.com (Kamran Kordi) To: richard@vocalis.com The 16 digit credit card numbers have now been generated and a copy is enclosed for your information. Generating these numbers was not as easy a task as it seemed at the beginning. Neither a random approach nor a simple methodical approach was found to be the answer. However, a sophisticated methodical approach answered our prayers and produced what we were after. The checksum digit at the end of the string was computed according to your formula; but your description of the methodology is incorrect. That is step3, where, the text is not what the so called algorithmically expressed operations do. ***************************16 digit numbers start here *********************** 0500 8824 0710 2777 0490 2332 8674 1248 0510 0620 7667 3063 0480 8636 0800 9882 0520 2592 0833 4444 0470 1191 0364 9173 0530 9627 0888 9258 0460 6894 1601 2055 0540 2622 7895 8262 0455 3633 2402 8994 0555 0744 1721 0154 0440 1681 6295 4013 0560 0773 8387 0250 0430 9686 2602 6254 0570 3367 1735 1512 1501 0330 6973 4096 1491 1765 7405 2082 1511 2712 1274 1075 1481 6604 8812 7025 1521 3892 1201 5817 1471 0873 9933 1177 1531 1611 2666 7589 1461 2722 0290 7171 1541 8314 6395 9249 1456 9912 9725 2063 1556 8287 3613 9650 1441 2682 2366 3160 1561 2672 3583 9796 1431 1371 7635 1754 1571 9779 4095 9865 2502 0890 0300 6881 2492 2632 6096 2266 2512 7386 4186 5995 2482 1671 9896 1997 2522 6624 2093 1166 2472 0600 0864 3990 2532 3623 3185 3140 2462 1183 1811 9853 2542 8397 6634 5138 2457 3423 0670 0089 2557 1781 1365 7073 2442 8369 8616 5198 2562 1665 7368 2262 2432 0644 8695 8697 2572 0165 1591 0008 3503 3393 9315 6763 3493 1581 8668 9356 3513 3373 0400 6984 3483 1331 0764 7082 3523 3334 8802 8983 3473 9607 8626 0064 3533 0610 8714 6744 3463 2612 6195 0283 3543 6385 7875 5345 3458 0264 0590 7268 3558 8324 9325 7998 3443 1135 8304 2171 3563 7673 0320 9560 3433 9963 0234 1029 3573 3383 0220 7985 4504 0390 1291 7853 4494 9796 0420 0055 4514 1311 2322 9472 4484 7196 1211 9026 4524 0380 0110 9833 4474 2312 1301 6991 4534 2372 0664 4630 4464 8876 0680 9870 4544 0280 7396 7065 4459 7097 0823 0176 4394 0410 9705 2153 4384 1791 8685 1713 4294 2292 9923 2043 4284 1691 7296 9059 4194 9298 6775 0026 5505 8098 0844 1052 5495 8834 2184 6460 5515 1391 6594 8152 5485 2302 2692 8220 5525 9835 7188 4156 5475 6874 7286 9048 5535 1381 7615 9078 5465 8224 8297 9188 5545 0273 1421 8169 5683 8795 6614 0075 5693 3293 2392 7677 5783 2275 7776 0144 5793 1701 8278 9454 5889 1281 0370 3264 5893 9803 8865 3174 6506 9675 8376 9555 6496 8724 0754 7884 6516 7335 1235 2121 6486 6404 0034 1080 6526 1631 1265 8057 6476 8606 3276 2992 6536 8845 7277 8261 6466 0700 0310 8146 6559 7694 0790 8062 6564 0720 9225 9062 6434 1035 7303 3557 6574 9398 1755 7160 6424 8785 1645 1048 6584 7723 7974 9158 6414 8202 3193 8083 7507 9944 9407 5358 7497 3792 1801 9340 7517 3782 0780 8040 7487 7313 2382 2079 7527 9305 1745 7807 7477 1125 7605 2163 7537 0100 1321 8660 7467 6794 0134 9982 7565 2582 9696 2141 7435 7375 1401 9147 7575 8197 9198 9174 7425 0654 0190 0241 7585 9388 0900 9086 7415 7323 9617 9030 7595 7713 8704 9267 8508 3403 8855 2002 8498 9203 8189 9849 8518 9786 0182 6089 8488 6285 1411 3077 8528 7703 7684 3680 8478 2412 9825 4083 8538 2422 9669 3890 8468 6187 9288 3081 8566 0210 7625 9584 8436 2192 8778 3081 8576 3593 9099 9164 8426 1774 0124 3469 8586 1621 0580 0836 8416 1114 0854 9315 8596 9377 3413 7579 9509 2891 9715 5985 9499 3283 9213 9360 9519 9115 0810 0016 9489 9101 9813 4943 9529 0630 0091 0043 9479 1092 6374 8172 9539 3094 8212 9133 9469 0200 2702 1263 9567 9279 9901 9649 9437 3603 0690 6068 9577 1711 2223 7376 9427 9954 0734 7654 9587 2282 8406 1065 9417 6784 1221 8076 9597 8975 9976 9998 *************************16 digit numbers end here *************************** Date: Tue, 16 Jul 1996 15:53:10 +0100 From: kamran.kordi@gecm.com (Kamran Kordi) To: richard@vocalis.com Richard, Please find enclosed a better set of 6 digit PINs and disregard the first one: Cheers Kamran *******************************Start************************************* 000100 002003 004005 006007 011012 013014 015016 019021 022023 024025 026027 030310 032033 034035 036037 041042 043044 045046 049050 051052 053054 057058 059061 062063 066067 068069 070710 072073 076077 078079 081082 085086 087088 089090 091092 095096 097098 099111 112102 115116 117118 119120 122123 127128 129132 133134 137138 139140 141420 143144 147148 149152 153154 155156 159160 161621 163164 167168 169172 173174 175176 181820 183184 185186 193194 195196 199201 222300 224211 226227 229214 236237 248249 255256 257217 265266 272730 283281 284285 293290 296297 298299 333411 336302 337322 338339 347348 354352 355356 364365 366367 374370 378379 384381 389390 395393 398399 444540 447415 449404 456422 457441 466443 467460 469463 475472 485480 486481 488489 495492 496497 498499 555601 557500 559523 565611 566502 567524 568562 569563 576536 577578 579580 586581 587583 588589 596592 666700 668605 669612 676613 677614 678615 679662 687673 688633 689681 697682 698690 699722 777811 779733 787702 788723 789745 798785 799801 888922 898804 899900 *******************************End*************************************** Credit Card Numbers Analysis: 1) frequency of digits by column position: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 15 0 10 13 23 5 18 15 38 6 22 21 15 45 3 19 1 15 1 14 13 27 13 16 20 22 13 20 16 14 29 6 10 2 15 2 14 13 20 18 17 24 12 22 18 11 15 16 6 15 3 15 2 18 18 17 31 14 24 6 22 10 14 13 7 6 21 4 15 65 10 20 0 6 4 24 2 10 3 24 7 5 20 17 5 15 74 10 18 0 4 2 19 0 5 4 31 7 7 23 14 6 15 2 18 17 10 31 7 8 10 27 13 16 9 8 29 15 7 15 2 18 17 12 25 19 9 18 19 16 6 17 6 21 12 8 15 2 19 10 19 12 24 4 21 19 17 8 16 13 23 15 9 15 0 19 11 22 5 29 3 21 7 27 3 37 14 13 12 2) frequency of digit transitions: (# is silence) # 0 1 2 3 4 5 6 7 8 9 Total # : 0 91 78 62 51 24 22 44 62 71 95 450 0 : 68 21 21 23 18 20 20 21 21 23 12 268 1 : 59 18 17 22 21 21 23 20 24 12 12 249 2 : 63 18 18 17 18 21 22 23 14 12 12 238 3 : 77 17 16 14 17 22 22 16 13 13 11 238 4 : 85 17 15 12 15 19 16 14 12 13 14 232 5 : 82 12 13 12 15 19 19 15 15 18 13 233 6 : 56 19 13 17 19 22 23 17 17 16 16 235 7 : 44 16 17 16 21 21 23 23 19 16 16 232 8 : 37 19 20 23 23 21 21 21 16 19 17 237 9 : 29 20 21 20 20 22 22 21 19 24 20 238 3) there are 1285 tridigits (including silence as a 'digit') out of a possible 11**3 = 1331