In mathematics, a **vampire number** is a number that can be obtained by multiplying two numbers of equal length (the fangs) whith every digit occurs in both factors.

## Definition

The vampire number is a composite natural number v, with an even number of digits n, that can be factored into two integers x and y each with n/2 digits and not both with trailing zeroes, where v contains precisely all the digits from x and from y, in any order, counting multiplicity. x and y are called the fangs.

## Origin

Vampire numbers first appeared in a 1994 post by Clifford A. Pickover to the Usenet group sci.math, and the article he later wrote was published in chapter 30 of his book *Keys to Infinity*.

## Examples

For example: 1260 is a vampire number, with 21 and 60 as fangs, since 21 × 60 = 1260.

However, 126000 (which can be expressed as 210 × 600) is not, as both 210 and 600 have trailing zeroes.

Similarly, 1023 (which can be expressed as 31 × 33) is not, because although 1023 contains all the digits of 31 and 33, the list of digits of the factors does not coincide with the list of digits of the original number.

## List

- 21 x 60 = 1260
- 15 x 93 = 1395
- 35 x 41 = 1435
- 30 x 51 = 1530
- 21 x 87 = 1827
- 27 x 81 = 2187
- 80 x 86 = 6880
- 102510, 104260, 105210, 105264, 105750, 108135, 110758, 115672, 116725, 117067, 118440, 120600, 123354, 124483, 125248, 125433, 125460, 125500, ... (sequence A014575 in OEIS)

## References

- Pickover, Clifford A. (1995).
*Keys to Infinity*. Wiley. ISBN 0-471-19334-8 - Pickover's original post describing vampire numbers
- Andersen, Jens K.
*Vampire Numbers* - Rivera, Carlos.
*The Prime-Vampire numbers* - Schneider, Walter.
*Vampire Numbers*