These are all the possible six digit candidates for membership in the vampire club! My computer program searches by multiplying all 405,450 possible combinations. (100 x 100, then 100 x 101, 100 x 102 up to 100 x 999. Then it starts over at 101 x 101, 101 x 102 up to 101 x 999, etc.) This generates a list which then must be filtered to screen out false and virtual vampire numbers. Some of the vampire numbers found are disqualified because they are false vampire numbers, meaning they are padded with zeros. For example, the first one disqualified is # 6, 139500, since it is the product of 150 x 930. Since 15 x 93 = 1395, adding zeros to 15 and 93 to get 150 x 930 = 139500 is like sneaking in the back door to the club. No dignity here, so the bouncer finds this false vampire number and throws it out! There are seven of these "sneak-in's" that get thrown out. (#'s 6, 23, 24, 52, 60, 77, 145)
This brings us to the last "extra" vampire number that shows up in our list of possibilites. The vampire number 125460 shows up twice! Twins?! This vampire number has two sets of factors, since 204 x 615 = 125460, and 246 x 510 = 125460. There may be two ways to arrive at this number, but it's still only one number, so we can't count it twice. The bouncer throws the mirror twin out of the club, since this is only a virtual vampire number. Minus one more from our total.
156 candidates - 7 false vampires = 149 candidates - 1 virtual vampire = 148 true six digit vampire numbers.
List ordered by first factor | List ordered by vampire number |
1. 135 x 801 = 108135 | 201 x 510 = 102510 |
2. 140 x 926 = 129640 | 260 x 401 = 104260 |
3. 141 x 840 = 118440 | 210 x 501 = 105210 |
4. 146 x 938 = 136948 | 204 x 516 = 105264 |
5. 150 x 705 = 105750 | 150 x 705 = 105750 |
6. 150 x 930 = 139500 disqualified | 135 x 801 = 108135 |
7. 152 x 761 = 115672 | 158 x 701 = 110758 |
8. 152 x 824 = 125248 | 152 x 761 = 115672 |
9. 156 x 942 = 146952 | 161 x 725 = 116725 |
10. 158 x 701 = 110758 | 167 x 701 = 117067 |
11. 161 x 725 = 116725 | 141 x 840 = 118440 |
12. 165 x 951 = 156915 | 201 x 600 = 120600 |
13. 167 x 701 = 117067 | 231 x 534 = 123354 |
14. 176 x 926 = 162976 | 281 x 443 = 124483 |
15. 179 x 725 = 129775 | 152 x 824 = 125248 |
16. 201 x 510 = 102510 | 231 x 543 = 125433 |
17. 201 x 600 = 120600 | 204 x 615 = 125460 |
18. 201 x 627 = 126027 | 246 x 510 = 125460 disqualified(virtual twin) |
19. 201 x 897 = 180297 | 251 x 500 = 125500 |
20. 204 x 516 = 105264 | 210 x 600 = 126000 disqualified |
21. 204 x 615 = 125460 | 201 x 627 = 126027 |
22. 210 x 501 = 105210 | 261 x 486 = 126846 |
23. 210 x 600 = 126000 disqualified | 140 x 926 = 129640 |
24. 210 x 870 = 182700 disqualified | 179 x 725 = 129775 |
25. 210 x 906 = 190260 | 311 x 422 = 131242 |
26. 210 x 915 = 192150 | 323 x 410 = 132430 |
27. 215 x 635 = 136525 | 315 x 423 = 133245 |
28. 216 x 864 = 186624 | 317 x 425 = 134725 |
29. 216 x 981 = 211896 | 231 x 588 = 135828 |
30. 221 x 782 = 172822 | 351 x 387 = 135837 |
31. 225 x 801 = 180225 | 215 x 635 = 136525 |
32. 225 x 810 = 182250 | 146 x 938 = 136948 |
33. 231 x 534 = 123354 | 150 x 930 = 139500 disqualified |
34. 231 x 543 = 125433 | 350 x 401 = 140350 |
35. 231 x 588 = 135828 | 350 x 410 = 143500 disqualified |
36. 231 x 750 = 173250 | 351 x 414 = 145314 |
37. 231 x 759 = 175329 | 317 x 461 = 146137 |
38. 240 x 651 = 156240 | 156 x 942 = 146952 |
39. 246 x 510 = 125460 disqualified (virtual twin of #21) | 300 x 501 = 150300 |
40. 248 x 881 = 218488 | 251 x 608 = 152608 |
41. 248 x 926 = 229648 | 261 x 585 = 152685 |
42. 251 x 500 = 125500 | 300 x 510 = 153000 disqualified |
43. 251 x 608 = 152608 | 356 x 431 = 153436 |
44. 251 x 860 = 215860 | 240 x 651 = 156240 |
45. 252 x 801 = 201852 | 269 x 581 = 156289 |
46. 255 x 807 = 205785 | 165 x 951 = 156915 |
47. 260 x 401 = 104260 | 176 x 926 = 162976 |
48. 261 x 486 = 126846 | 396 x 414 = 163944 |
49. 261 x 585 = 152685 | 221 x 782 = 172822 |
50. 269 x 581 = 156289 | 231 x 750 = 173250 |
51. 269 x 842 = 226498 | 371 x 470 = 174370 |
52. 270 x 810 = 218700 disqualified | 231 x 759 = 175329 |
53. 275 x 719 = 197725 | 225 x 801 = 180225 |
54. 276 x 822 = 226872 | 201 x 897 = 180297 |
55. 281 x 443 = 124483 | 225 x 810 = 182250 |
56. 281 x 650 = 182650 | 281 x 650 = 182650 |
57. 284 x 926 = 262984 | 210 x 870 = 182700 disqualified |
58. 296 x 851 = 251896 | 216 x 864 = 186624 |
59. 300 x 501 = 150300 | 210 x 906 = 190260 |
60. 300 x 510 = 153000 disqualified | 210 x 915 = 192150 |
61. 311 x 422 = 131242 | 327 x 591 = 193257 |
62. 315 x 423 = 133245 | 395 x 491 = 193945 |
63. 317 x 425 = 134725 | 275 x 719 = 197725 |
64. 317 x 461 = 146137 | 252 x 801 = 201852 |
65. 320 x 926 = 296320 | 255 x 807 = 205785 |
66. 321 x 678 = 217638 | 216 x 981 = 211896 |
67. 321 x 975 = 312975 | 341 x 626 = 213466 |
68. 323 x 410 = 132430 | 251 x 860 = 215860 |
69. 323 x 671 = 216733 | 323 x 671 = 216733 |
70. 323 x 806 = 260338 | 321 x 678 = 217638 |
71. 327 x 591 = 193257 | 248 x 881 = 218488 |
72. 336 x 951 = 319536 | 270 x 810 = 218700 disqualified |
73. 338 x 692 = 233896 | 269 x 842 = 226498 |
74. 341 x 626 = 213466 | 276 x 822 = 226872 |
75. 342 x 963 = 329346 | 248 x 926 = 229648 |
76. 350 x 401 = 140350 | 338 x 692 = 233896 |
77. 350 x 410 = 143500 disqualified | 461 x 524 = 241564 |
78. 350 x 725 = 253750 | 422 x 581 = 245182 |
79. 351 x 387 = 135837 | 296 x 851 = 251896 |
80. 351 x 414 = 145314 | 350 x 725 = 253750 |
81. 351 x 900 = 315900 | 470 x 542 = 254740 |
82. 351 x 909 = 319059 | 323 x 806 = 260338 |
83. 356 x 431 = 153436 | 284 x 926 = 262984 |
84. 356 x 926 = 329656 | 437 x 602 = 263074 |
85. 360 x 936 = 336960 | 489 x 582 = 284598 |
86. 366 x 948 = 346968 | 420 x 678 = 284760 |
87. 369 x 981 = 361989 | 468 x 612 = 286416 |
88. 371 x 470 = 174370 | 320 x 926 = 296320 |
89. 381 x 969 = 369189 | 431 x 707 = 304717 |
90. 383 x 971 = 371893 | 431 x 725 = 312475 |
91. 392 x 863 = 338296 | 321 x 975 = 312975 |
92. 392 x 926 = 362992 | 534 x 591 = 315594 |
93. 395 x 491 = 193945 | 351 x 900 = 315900 |
94. 396 x 414 = 163944 | 351 x 909 = 319059 |
95. 420 x 678 = 284760 | 336 x 951 = 319536 |
96. 422 x 581 = 245182 | 524 x 623 = 326452 |
97. 431 x 707 = 304717 | 342 x 963 = 329346 |
98. 431 x 725 = 312475 | 356 x 926 = 329656 |
99. 431 x 878 = 378418 | 530 x 635 = 336550 |
100. 432 x 891 = 384912 | 360 x 936 = 336960 |
101. 435 x 870 = 378450 | 392 x 863 = 338296 |
102. 437 x 602 = 263074 | 533 x 641 = 341653 |
103. 446 x 908 = 404968 | 366 x 948 = 346968 |
104. 461 x 524 = 241564 | 369 x 981 = 361989 |
105. 464 x 926 = 429664 | 392 x 926 = 362992 |
106. 465 x 831 = 386415 | 533 x 686 = 365638 |
107. 468 x 612 = 286416 | 585 x 630 = 368550 |
108. 468 x 891 = 416988 | 381 x 969 = 369189 |
109. 470 x 542 = 254740 | 383 x 971 = 371893 |
110. 473 x 800 = 378400 | 473 x 800 = 378400 |
111. 476 x 941 = 447916 | 431 x 878 = 378418 |
112. 482 x 890 = 428980 | 435 x 870 = 378450 |
113. 489 x 582 = 284598 | 432 x 891 = 384912 |
114. 491 x 845 = 414895 | 465 x 831 = 386415 |
115. 524 x 623 = 326452 | 593 x 662 = 392566 |
116. 530 x 635 = 336550 | 446 x 908 = 404968 |
117. 533 x 641 = 341653 | 491 x 845 = 414895 |
118. 533 x 686 = 365638 | 641 x 650 = 416650 |
119. 534 x 591 = 315594 | 468 x 891 = 416988 |
120. 540 x 846 = 456840 | 482 x 890 = 428980 |
121. 545 x 899 = 489955 | 464 x 926 = 429664 |
122. 546 x 840 = 458640 | 476 x 941 = 447916 |
123. 549 x 891 = 489159 | 540 x 846 = 456840 |
124. 563 x 953 = 536539 | 650 x 704 = 457600 |
125. 570 x 834 = 475380 | 546 x 840 = 458640 |
126. 572 x 926 = 529672 | 570 x 834 = 475380 |
127. 585 x 630 = 368550 | 624 x 780 = 486720 |
128. 588 x 951 = 559188 | 549 x 891 = 489159 |
129. 590 x 845 = 498550 | 545 x 899 = 489955 |
130. 593 x 662 = 392566 | 590 x 845 = 498550 |
131. 624 x 780 = 486720 | 681 x 759 = 516879 |
132. 630 x 855 = 538650 | 572 x 926 = 529672 |
133. 641 x 650 = 416650 | 563 x 953 = 536539 |
134. 650 x 704 = 457600 | 630 x 855 = 538650 |
135. 650 x 875 = 568750 | 588 x 951 = 559188 |
136. 650 x 983 = 638950 | 657 x 864 = 567648 |
137. 657 x 864 = 567648 | 650 x 875 = 568750 |
138. 680 x 926 = 629680 | 680 x 926 = 629680 |
139. 681 x 759 = 516879 | 650 x 983 = 638950 |
140. 720 x 936 = 673920 | 720 x 936 = 673920 |
141. 750 x 906 = 679500 | 750 x 906 = 679500 |
142. 765 x 963 = 736695 | 800 x 860 = 688000 disqualified |
143. 776 x 992 = 769792 | 788 x 926 = 729688 |
144. 788 x 926 = 729688 | 765 x 963 = 736695 |
145. 800 x 860 = 688000 disqualified | 843 x 876 = 738468 |
146. 807 x 984 = 794088 | 776 x 992 = 769792 |
147. 825 x 957 = 789525 | 875 x 902 = 789250 |
148. 843 x 876 = 738468 | 825 x 957 = 789525 |
149. 855 x 927 = 792585 | 855 x 927 = 792585 |
150. 858 x 951 = 815958 | 807 x 984 = 794088 |
151. 875 x 902 = 789250 | 891 x 909 = 809919 |
152. 891 x 909 = 809919 | 894 x 906 = 809964 |
153. 891 x 945 = 841995 | 858 x 951 = 815958 |
154. 894 x 906 = 809964 | 896 x 926 = 829696 |
155. 896 x 926 = 829696 | 891 x 945 = 841995 |
156. 953 x 986 = 939658 | 953 x 986 = 939658 |
My thanks to Eric W. Weisstein of the University of Virginia Astronomy Dept., Charlottesville, VA, for assistance in helping decide 6 digit vampire club membership.
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