Vampire Numbers - Numberphile

TL;DR

Vampire numbers are numbers that can be split into two numbers that multiply together to create the original number, using all the digits of the original number.

Transcript

DR. JAMES GRIME: We're going to talk about vampires. Yes, math and vampires. PROFESSOR ED COPELAND: Well, my youngest daughter, today is having two teeth out. So she probably won't like this one very much. A vampire number is where-- DR. JAMES GRIME: You have two numbers that are the same length-- PROFESSOR ED COPELAND: --a number with an even numb... Read More

Key Insights

• #️⃣ Vampire numbers are a mathematical concept involving numbers that can be split into two multiplying numbers.
• 💨 Vampire numbers can have multiple ways to split into fangs, using the same digits in different order.
• #️⃣ Prime vampire numbers have prime fangs, which are prime numbers that multiply together to form the original number.
• #️⃣ Trailing zeroes at the end of each pair of fangs are not allowed in vampire numbers. This rule prevents the creation of additional numbers that do not fit the vampire number criteria.
• 🧛 In folklore, vampires were said to suffer from a compulsion to count called arithmomania, which may have inspired the concept of vampire numbers.

Questions & Answers

Q: How are vampire numbers defined?

Vampire numbers are even-digit numbers that can be split into two two-digit numbers, which when multiplied together, produce the original number, utilizing all the digits in the original number.

Q: Can vampire numbers have multiple ways to split into fangs?

Yes, vampire numbers can have multiple ways to split into fangs. The same set of digits can be used in a different order to form different fangs that multiply to produce the original number.

Q: Can vampire numbers have prime fangs?

Yes, vampire numbers can have prime fangs. In such cases, the fangs are prime numbers, and the vampire number itself is called a prime vampire number.

Q: Are trailing zeroes allowed in vampire numbers?

No, trailing zeroes are not allowed in vampire numbers. Each pair of fangs must not have a trailing zero at the end to be considered a valid vampire number.

Summary & Key Takeaways

• Vampire numbers are numbers that can be expressed as the product of two two-digit numbers, using all the digits of the original number.

• There can be multiple ways to split a vampire number into its "fangs" (the two multiplying numbers), using the same digits in different order.

• Vampire numbers can also have prime fangs, where the fangs are prime numbers.