GENERATE PRIME FACTORS by Uncle Bob

Although quite short, this kata is fascinating in the way it shows how ‘if’ statements
become ‘while’ statements as the number of test cases increase.  It’s also a
wonderful example of how algorithms sometimes become simpler as they become
more general.

I stumbled upon this little kata one evening when my son was in 7th grade.  He
had just discovered that all numbers can be broken down into a product of primes
and was interested in exploring this further.  So I wrote a little ruby program, test-
first, and was stunned by how the algorithm evolved.

I have done this particular kata in Java 5.0.  This should give you a feel for the 
power and convenience of some of the new features.

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The Requirements

Write a class named “PrimeFactors” that has one static method: generate.
The generate method takes an integer argument and returns a List<Integer>.  
That list contains the prime factors in numerical sequence.

Source: http://butunclebob.com/ArticleS.UncleBob.ThePrimeFactorsKata

Prime Factor Definition: (http://en.wikipedia.org/wiki/Prime_factor)

In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization. A prime factor can be visualized by understanding Euclid's geometric position. He saw a whole number as a line segment, which has a smallest line segment greater than 1 that can divide equally into it.
For a prime factor p of n, the multiplicity of p is the largest exponent a for which pa divides n. The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicity. The fundamental theorem of arithmetic says that every positive integer has a unique prime factorization.
To shorten prime factorization, numbers are often expressed in powers, so

For a positive integer n, the number of prime factors of n and the sum of the prime factors of n (not counting multiplicity) are examples of arithmetic functions of n that are additive but not completely additive.