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Thursday, October 30, 2014

Throwback Fact of the Week - Vampire Numbers - 10/30/14

Vampire numbers were first defined by Clifford Pickover in 1994. 

A vampire number is a composite whole number with an even number of digits, n. The vampire number has form v = xy where the digits x and y each have n/2 digits. These digits consist only of the digits in the vampire number, but in any order. Note that x and y are not allowed to both end in trailing zeros. 

1260 is the smallest vampire number.
 v = xy
1260 = 21*60

You'll notice that in this case, the vampire number has 4 digits; x and y each have 2 digits, and those digits consist of a re-arrangement of the digits in the vampire number. 

The digits x and y are known as the fangs of the vampire number. Vampire numbers sometimes have multiple pairs of fangs that fit the rules for forming the vampire number. Such as 125460 = 204 × 615 but it also equals 246 × 510.

An even more interesting type of vampire number would be a vampire number where its fangs are also its prime factors. For example, 117067 = 167 × 701, where 167 and 701 are the prime factors of 117067, making this number a prime vampire number! 

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