105,750 is one such number: it equals the product of its two fangs, 150 and 705. Since 105,750 = 150 × 705, the digits of the two factors together are precisely the digits of 105,750. More precisely, a vampire number is a composite number n with an even number of digits that is the product of two integers p and q, called "fangs," each with the same number of digits, such that n contains all the digits of p and q.
The first vampire numbers are 1,260, 1,395, 1,435, 1,530, 1,827, 2,187, 6,880, 102,510… The more digits they have, the more of them there are: seven have four digits, 148 have six digits, and 32,228 have eight digits… In fact, there are infinitely many.
Some can have several pairs of fangs.
For example, 125,460 = 204 × 615 = 246 × 510. Vampire numbers with five pairs of fangs are known: the smallest is 24,959,017,348,650.
There is something even "more disturbing": double vampire numbers! They are vampire numbers whose fangs are themselves vampire numbers. The smallest is:
1,047,527,295,416,280 = 25,198,740 × 41,570,622 = (2,940 × 8,571) × (5,601 × 7,422).
