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Property 
Definition 
Example

Multiple of 3 
Each digit in the number is a multiple of three (remember 3 * 0 = 0!). 

Power of 2 
Each digit in the number is a power of two (remember 2^{0}=1!). 

Consecutive digits 
A number has n consecutive digits when it contains n consecutive integers, regardless of order. 

Vampire numbers 
A number is a vampire number if there exists a factorization of it using only the digits of the original number. The factorization is called the "fangs" of the original number. 

Prime numbers 
The number can only be divided by itself and one. Dividing by any other number causes a remainder. There are exactly 5,761,455 prime numbers under 100 million. 

Palindrome 
The numbers digits are symmetric so that the first and last digits are the same, the second and secondtolast digits are the same, etc. This property occurs in 0.010% of 8digit numbers. 

Even/Odd 
If a number has all odd digits or all even digits, the property is noted. This occurs in 0.39% of 8digits numbers. 

Sum of digits 
If the sum of the digits is less than 25 or greater than 47, then this property is noted. 

Fibonacci sequence 
A number in the Fibonacci sequence is the sum of the two previous numbers in that sequence. The first two are 1 and 1, so the next number would be 2, followed by 3, then 5, and so on. 

Unique digits 
When a particular digit only appears once, that is a unique digits. If there are less than three or more than six unique digits, this property is activated. 

Forward runs 
When consecutive digits are consecutive increasing integers (for runs longer than two), then this property is activated. 

Backward runs 
When consecutive digits are consecutive decreasing integers (for runs longer than two), then this property is activated. 

Factorial 
The factorial of n is the product of:
n*(n1)*(n2) *... * (n  (n 2)) * 1 

Tuples together 
A tuple is a pair, triple, 4ofakind, etc. When the unordered number has a repeated digit, it has a tuple together. 

Tuples 
When the ordered (or sorted) number has a repeated digit, the unordered number has a tuple apart. In other words, this is a tuple "together or apart". 
