Six digit vampire numbers


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 factorList ordered by vampire number
1. 135 x 801 = 108135201 x 510 = 102510
2. 140 x 926 = 129640260 x 401 = 104260
3. 141 x 840 = 118440210 x 501 = 105210
4. 146 x 938 = 136948204 x 516 = 105264
5. 150 x 705 = 105750150 x 705 = 105750
6. 150 x 930 = 139500 disqualified135 x 801 = 108135
7. 152 x 761 = 115672158 x 701 = 110758
8. 152 x 824 = 125248152 x 761 = 115672
9. 156 x 942 = 146952161 x 725 = 116725
10. 158 x 701 = 110758167 x 701 = 117067
11. 161 x 725 = 116725141 x 840 = 118440
12. 165 x 951 = 156915201 x 600 = 120600
13. 167 x 701 = 117067231 x 534 = 123354
14. 176 x 926 = 162976281 x 443 = 124483
15. 179 x 725 = 129775152 x 824 = 125248
16. 201 x 510 = 102510231 x 543 = 125433
17. 201 x 600 = 120600204 x 615 = 125460
18. 201 x 627 = 126027246 x 510 = 125460 disqualified(virtual twin)
19. 201 x 897 = 180297251 x 500 = 125500
20. 204 x 516 = 105264210 x 600 = 126000 disqualified
21. 204 x 615 = 125460201 x 627 = 126027
22. 210 x 501 = 105210261 x 486 = 126846
23. 210 x 600 = 126000 disqualified140 x 926 = 129640
24. 210 x 870 = 182700 disqualified179 x 725 = 129775
25. 210 x 906 = 190260311 x 422 = 131242
26. 210 x 915 = 192150323 x 410 = 132430
27. 215 x 635 = 136525315 x 423 = 133245
28. 216 x 864 = 186624317 x 425 = 134725
29. 216 x 981 = 211896231 x 588 = 135828
30. 221 x 782 = 172822351 x 387 = 135837
31. 225 x 801 = 180225215 x 635 = 136525
32. 225 x 810 = 182250146 x 938 = 136948
33. 231 x 534 = 123354150 x 930 = 139500 disqualified
34. 231 x 543 = 125433350 x 401 = 140350
35. 231 x 588 = 135828350 x 410 = 143500 disqualified
36. 231 x 750 = 173250351 x 414 = 145314
37. 231 x 759 = 175329317 x 461 = 146137
38. 240 x 651 = 156240156 x 942 = 146952
39. 246 x 510 = 125460 disqualified (virtual twin of #21)300 x 501 = 150300
40. 248 x 881 = 218488251 x 608 = 152608
41. 248 x 926 = 229648261 x 585 = 152685
42. 251 x 500 = 125500300 x 510 = 153000 disqualified
43. 251 x 608 = 152608356 x 431 = 153436
44. 251 x 860 = 215860240 x 651 = 156240
45. 252 x 801 = 201852269 x 581 = 156289
46. 255 x 807 = 205785165 x 951 = 156915
47. 260 x 401 = 104260176 x 926 = 162976
48. 261 x 486 = 126846396 x 414 = 163944
49. 261 x 585 = 152685221 x 782 = 172822
50. 269 x 581 = 156289231 x 750 = 173250
51. 269 x 842 = 226498371 x 470 = 174370
52. 270 x 810 = 218700 disqualified231 x 759 = 175329
53. 275 x 719 = 197725225 x 801 = 180225
54. 276 x 822 = 226872201 x 897 = 180297
55. 281 x 443 = 124483225 x 810 = 182250
56. 281 x 650 = 182650281 x 650 = 182650
57. 284 x 926 = 262984210 x 870 = 182700 disqualified
58. 296 x 851 = 251896216 x 864 = 186624
59. 300 x 501 = 150300210 x 906 = 190260
60. 300 x 510 = 153000 disqualified210 x 915 = 192150
61. 311 x 422 = 131242327 x 591 = 193257
62. 315 x 423 = 133245395 x 491 = 193945
63. 317 x 425 = 134725275 x 719 = 197725
64. 317 x 461 = 146137252 x 801 = 201852
65. 320 x 926 = 296320255 x 807 = 205785
66. 321 x 678 = 217638216 x 981 = 211896
67. 321 x 975 = 312975341 x 626 = 213466
68. 323 x 410 = 132430251 x 860 = 215860
69. 323 x 671 = 216733323 x 671 = 216733
70. 323 x 806 = 260338321 x 678 = 217638
71. 327 x 591 = 193257248 x 881 = 218488
72. 336 x 951 = 319536270 x 810 = 218700 disqualified
73. 338 x 692 = 233896269 x 842 = 226498
74. 341 x 626 = 213466276 x 822 = 226872
75. 342 x 963 = 329346248 x 926 = 229648
76. 350 x 401 = 140350338 x 692 = 233896
77. 350 x 410 = 143500 disqualified461 x 524 = 241564
78. 350 x 725 = 253750422 x 581 = 245182
79. 351 x 387 = 135837296 x 851 = 251896
80. 351 x 414 = 145314350 x 725 = 253750
81. 351 x 900 = 315900470 x 542 = 254740
82. 351 x 909 = 319059323 x 806 = 260338
83. 356 x 431 = 153436284 x 926 = 262984
84. 356 x 926 = 329656437 x 602 = 263074
85. 360 x 936 = 336960489 x 582 = 284598
86. 366 x 948 = 346968420 x 678 = 284760
87. 369 x 981 = 361989468 x 612 = 286416
88. 371 x 470 = 174370320 x 926 = 296320
89. 381 x 969 = 369189431 x 707 = 304717
90. 383 x 971 = 371893431 x 725 = 312475
91. 392 x 863 = 338296321 x 975 = 312975
92. 392 x 926 = 362992534 x 591 = 315594
93. 395 x 491 = 193945351 x 900 = 315900
94. 396 x 414 = 163944351 x 909 = 319059
95. 420 x 678 = 284760336 x 951 = 319536
96. 422 x 581 = 245182524 x 623 = 326452
97. 431 x 707 = 304717342 x 963 = 329346
98. 431 x 725 = 312475356 x 926 = 329656
99. 431 x 878 = 378418530 x 635 = 336550
100. 432 x 891 = 384912360 x 936 = 336960
101. 435 x 870 = 378450392 x 863 = 338296
102. 437 x 602 = 263074533 x 641 = 341653
103. 446 x 908 = 404968366 x 948 = 346968
104. 461 x 524 = 241564369 x 981 = 361989
105. 464 x 926 = 429664392 x 926 = 362992
106. 465 x 831 = 386415533 x 686 = 365638
107. 468 x 612 = 286416585 x 630 = 368550
108. 468 x 891 = 416988381 x 969 = 369189
109. 470 x 542 = 254740383 x 971 = 371893
110. 473 x 800 = 378400473 x 800 = 378400
111. 476 x 941 = 447916431 x 878 = 378418
112. 482 x 890 = 428980435 x 870 = 378450
113. 489 x 582 = 284598432 x 891 = 384912
114. 491 x 845 = 414895465 x 831 = 386415
115. 524 x 623 = 326452593 x 662 = 392566
116. 530 x 635 = 336550446 x 908 = 404968
117. 533 x 641 = 341653491 x 845 = 414895
118. 533 x 686 = 365638641 x 650 = 416650
119. 534 x 591 = 315594468 x 891 = 416988
120. 540 x 846 = 456840482 x 890 = 428980
121. 545 x 899 = 489955464 x 926 = 429664
122. 546 x 840 = 458640476 x 941 = 447916
123. 549 x 891 = 489159540 x 846 = 456840
124. 563 x 953 = 536539650 x 704 = 457600
125. 570 x 834 = 475380546 x 840 = 458640
126. 572 x 926 = 529672570 x 834 = 475380
127. 585 x 630 = 368550624 x 780 = 486720
128. 588 x 951 = 559188549 x 891 = 489159
129. 590 x 845 = 498550545 x 899 = 489955
130. 593 x 662 = 392566590 x 845 = 498550
131. 624 x 780 = 486720681 x 759 = 516879
132. 630 x 855 = 538650572 x 926 = 529672
133. 641 x 650 = 416650563 x 953 = 536539
134. 650 x 704 = 457600630 x 855 = 538650
135. 650 x 875 = 568750588 x 951 = 559188
136. 650 x 983 = 638950657 x 864 = 567648
137. 657 x 864 = 567648650 x 875 = 568750
138. 680 x 926 = 629680680 x 926 = 629680
139. 681 x 759 = 516879650 x 983 = 638950
140. 720 x 936 = 673920720 x 936 = 673920
141. 750 x 906 = 679500750 x 906 = 679500
142. 765 x 963 = 736695800 x 860 = 688000 disqualified
143. 776 x 992 = 769792788 x 926 = 729688
144. 788 x 926 = 729688765 x 963 = 736695
145. 800 x 860 = 688000 disqualified843 x 876 = 738468
146. 807 x 984 = 794088776 x 992 = 769792
147. 825 x 957 = 789525875 x 902 = 789250
148. 843 x 876 = 738468825 x 957 = 789525
149. 855 x 927 = 792585855 x 927 = 792585
150. 858 x 951 = 815958807 x 984 = 794088
151. 875 x 902 = 789250891 x 909 = 809919
152. 891 x 909 = 809919894 x 906 = 809964
153. 891 x 945 = 841995858 x 951 = 815958
154. 894 x 906 = 809964896 x 926 = 829696
155. 896 x 926 = 829696891 x 945 = 841995
156. 953 x 986 = 939658953 x 986 = 939658
156 - 8 = 148 true six digit vampire numbers.


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.


Home