## Sunday, 31 August 2008

### Vampire numbers

The vampire numbers were introduced by Clifford A. Pickover in 1994.

Definitions:

A vampire number is a number which can be written as a product of two numbers (called fangs), containing the same digits the same number of times as the vampire number. Example:

1827000 = 210 · 8700

A true vampire number is a vampire number which can be written with two fangs having the same number of digits and not both ending in 0.

Example:

1827 = 21 · 87

All vampire numbers (or just vampires) on the rest of this page are implicitly true. They must clearly have an even number of digits.

A prime vampire number (introduced by Carlos Rivera in 2002) is a true vampire number where the fangs are the prime factors.

The 7 vampires with 4 digits:

1260=21 · 60, 1395=15 · 93, 1435=35 · 41, 1530=30 · 51, 1827=21 · 87, 2187=27 · 81, 6880=80 · 86

The 5 prime vampires with 6 digits:

117067 = 167 · 701, 124483 = 281 · 443, 146137 = 317 · 461, 371893 = 383 · 971, 536539 = 563 · 953