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Vampire Number

mathworld.wolfram.com

65 pointsdustfinger13 comments

Are there vampire numbers that are palindromes? That would kinda contradict the vampire lore about mirrors. ;)

I find this disturbing because (do hear me out)

the fundamental arithmetic theorem would have me re-express all those numbers as the product of primes that they actually are.

I find pairing this list of primes (with powers) and splitting them into two groups to be ultimately arbitrary which blinds me from the significance of these 'kind' of numbers

i.e. i'm saying 'vampire numbers' are a lame kind of number because it involves arbitrary choices which are IMO stinky; they lack exactlyness

But why is it called a Vampire Number in the first place?

Because the digits of the multiplicands make up the digits of the vampire number- they look like any other number but have a secret, kind of like how vampires look like humans but have a secret. Here’s the text of the original post from the 1990’s describing them:

https://groups.google.com/g/sci.math/c/eCgYeC3aUbc/m/2haqpIE...

They aren’t particularly useful, but they are cool.

Thank you so much for sharing the link. I really enjoy reading Clifford Pickover's books. As a young teen, I was inspired by Wonders of Numbers and Surfing Through Hyperspace.

I am fond of the following explanations for the choice in naming [1]. However, your explanation came directly from the horses mouth ;-)

    1. The name “vampire” evokes the image of a creature that bites and multiplies. Similarly, vampire numbers “bite” a larger number into two smaller numbers (fangs) that, when multiplied together, recreate the original number.
    

    2. Clifford A. Pickover, who introduced the term in his book “Keys to Infinity,” often uses imaginative and evocative language to engage readers in mathematical concepts. The term “vampire numbers” reflects his creative approach to making mathematics more accessible and intriguing to a wide audience.

[1]: https://medium.com/@bhaskaravsupraja/ever-heard-of-vampire-n...

Cool, thanks!

Is this possible in binary? I can't get the result to have the same number of 1s and 0s as the two inputs.

I find lots of solutions in binary, e.g. 3 and 5: 011 * 101 = 001111. Or if you don't like leading zeroes, 22*29: 10110 * 11101 = 1001111110

A general solution is 2^n+9 and 2^(n+1)-2 for n >= 5

Good one, I didn't look as far as ten places.

To your point, they are coincidences of the base you are using, not really any inherently interesting imo

I was kind of hoping this might have something to with the Count from Sesame Street.

Or, also vampirically, a number where constructing it somehow requires adding up lots and lots of small numbers, like grains spilled on the floor.

This is the secret of eternal youth of the count. It was ALWAYS about numbers, but we took it jokingly

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