Vampire number facts for kids

Imagine a special kind of number that seems to "eat" its own digits! In the fun world of recreational mathematics, these are called vampire numbers. A vampire number is a composite number (a number that can be made by multiplying two smaller whole numbers) that has an even number of digits.

Here's the cool part: you can break a vampire number down into two smaller numbers, called its "fangs." Each fang must have exactly half the number of digits as the original vampire number. When you multiply these two fangs together, you get the original vampire number. But wait, there's more! If you take all the digits from both fangs and put them together, they must be exactly the same digits as in the original vampire number, just possibly in a different order. Also, both fangs cannot end in zero at the same time.

The very first vampire number ever found is 1260. Its fangs are 21 and 60. See? 21 multiplied by 60 equals 1260. And if you look at the digits of 21 and 60 (which are 2, 1, 6, 0), they are exactly the same digits as in 1260 (1, 2, 6, 0)!

These fascinating numbers were first talked about by a scientist named Clifford A. Pickover in 1994. He shared his discovery in a science discussion group online and later wrote about them in his book, Keys to Infinity.

What Are Vampire Numbers?

A vampire number is a special type of natural number (a positive whole number) that follows a few interesting rules. First, it must be a composite number, meaning it can be formed by multiplying two smaller whole numbers. Second, it must have an even number of digits, like 4, 6, or 8 digits.

How Do Vampire Numbers Work?

The most exciting part of a vampire number is how its "fangs" work. Let's use our example, 1260.

• 1260 has four digits (an even number).
• Its fangs are 21 and 60. Each fang has two digits, which is half of four.
• When you multiply the fangs: 21 × 60 = 1260. This gives you the original number.
• Now, gather all the digits from the fangs: 2, 1, 6, 0.
• Compare these to the digits of the original number: 1, 2, 6, 0. They are exactly the same digits, just in a different order! This is like a puzzle where all the pieces fit perfectly.

There's one more important rule: the two fangs cannot both end in zero. For example, 126000 is not a vampire number, even though 210 × 600 = 126000. Both 210 and 600 end in zero, so they don't count as valid fangs. Also, if you tried 21 × 6000, the fangs wouldn't have half the number of digits.

Discovering Vampire Numbers

Vampire numbers are quite rare, especially as they get larger. Here's a table showing how many vampire numbers exist for different lengths:

The First Vampire Numbers

The first few vampire numbers are:

• 1260 = 21 × 60
• 1395 = 15 × 93
• 1435 = 35 × 41
• 1530 = 30 × 51
• 1827 = 21 × 87
• 2187 = 27 × 81
• 6880 = 80 × 86
• 102510 = 201 × 510
• 104260 = 260 × 401
• 105210 = 210 × 501

The full list of vampire numbers starts with: 1260, 1395, 1435, 1530, 1827, 2187, 6880, 102510, 104260, 105210, 105264, 105750, 108135, 110758, 115672, 116725, 117067, 118440, 120600, 123354, 124483, 125248, 125433, 125460, 125500, ... (sequence A014575 in OEIS)

Scientists have even found patterns that create an endless supply of vampire numbers! For example:

• 1530 = 30 × 51
• 150300 = 300 × 501
• 15003000 = 3000 × 5001

And so on!

A computer programmer named Al Sweigart once calculated all the vampire numbers that have up to 10 digits.

Vampire Numbers with Many Fangs

Some vampire numbers are even more special because they have more than one pair of fangs!

• The first vampire number with two pairs of fangs is:

* 125460 = 204 × 615 = 246 × 510

• The first with three pairs of fangs is:

* 13078260 = 1620 × 8073 = 1863 × 7020 = 2070 × 6318

• The first with four pairs of fangs is:

* 16758243290880 = 1982736 × 8452080 = 2123856 × 7890480 = 2751840 × 6089832 = 2817360 × 5948208

• The first with five pairs of fangs is:

* 24959017348650 = 2947050 × 8469153 = 2949705 × 8461530 = 4125870 × 6049395 = 4129587 × 6043950 = 4230765 × 5899410

Vampire Numbers in Different Counting Systems

Our everyday numbers use a "base 10" system, meaning we count using ten digits (0-9). But numbers can exist in other "bases" or counting systems too! Vampire numbers can also be found in these different systems.

For example, in base 12, where we use twelve digits (0-9, plus A for ten, and B for eleven), there are also vampire numbers. One example is 10392BA45768, which has fangs 105628 and BA3974. Notice how all twelve digits are used exactly once!

See Also

• Friedman number