A vampire number is a composite number with an even number of digits that can be factored into two integers, called fangs, whose digits together form a permutation of the original number.
Definition and Properties
A vampire number is a natural number with an even number of digits that can be expressed as the product of two integers, each having half as many digits as the original number. These two integers are called fangs, and together they must contain exactly all the digits of the original number, in any order, counting multiplicity. Importantly, both fangs cannot end with zero simultaneously. For example, 1260 is a vampire number because 1260 = 21 × 60, and the digits 2, 1, 6, 0 are a permutation of the original number’s digits (1, 2, 6, 0)
These numbers follow a specific set of rules in recreational mathematics:
- Even digits: The vampire number must have an even number of digits.
- Half-length fangs: The two fangs must each have exactly half as many digits as the original number.
- Digit conservation: The digits from both fangs must exactly match the digits of the original number (in any order).
- No double zeros: Both fangs cannot simultaneously end in zero (because this would just result in multiple trailing zeros, and it effectively breaks the rules of digit alignment).
The first few vampire numbers include: 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, and 105264 = 204 × 516
Vampire numbers can have multiple distinct pairs of fangs, such as 125460 = 204 × 615 = 246 × 510.
Condition for a number to be vampire number:
- Has a pair number of digits. Lets call the number of digits : n
- You can obtain the number by multiplying two integers, x and y, each with n/2 digits. x and y are the fangs.
- Both fangs cannot end simultaneously in 0.
- The number can be made with all digits from x and y, in any order and only using each digit once.
Vampire numbers are a gateway into recreational number theory — the art of playing with numbers to discover surprising patterns. Searching for them builds skills in factoring, digit manipulation, and systematic problem-solving that apply directly in algebra and computer science.
References
Rivera, Carlos. “Puzzle 199. The Prime-Vampire Numbers.” 2002. https://www.primepuzzles.net/puzzles/puzz_199.htm.
“Vampire Number — Definition, Formula & Examples.” Accessed June 4, 2026. https://www.mathwords.com/v/vampire_number.htm.
“Vampire Number.” GeeksforGeeks, October 12, 2017. https://www.geeksforgeeks.org/dsa/vampire-number/.
“Vampire Number.” Rosetta Code, June 2, 2026. https://rosettacode.org/wiki/Vampire_number.
“Vampire Number.” Wikipedia, September 19, 2025. https://en.wikipedia.org/wiki/Vampire_number.
“Vampire Number Explained.” Everything.Explained. Accessed June 4, 2026. https://everything.explained.today/Vampire_number/.
Weisstein, Eric W. “Vampire Number.” From MathWorld–A Wolfram Resource. https://mathworld.wolfram.com/VampireNumber.html
Videos
The featured image on this page is from the Best Infographics website.