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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 20=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 second-to-last digits are the same, etc. This property occurs in 0.010% of 8-digit numbers.
Even/Odd If a number has all odd digits or all even digits, the property is noted. This occurs in 0.39% of 8-digits 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*(n-1)*(n-2) *... * (n - (n -2)) * 1
Tuples together A tuple is a pair, triple, 4-of-a-kind, 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".
These tests are all incorporated into the Universal Coolness Index, a single measure of a number's overall coolness.



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