I created a simple animation http://www.just-got-lucky.com/misc/output.gif" [Broken] that shows how, as you introduce each factor, you sieve out addends. (I tested this in Firefox.) There is kind of an interesting genetic-like growth pattern to the sieved addends. Its a 6Mb animated GIF so it may take a while to download the first time. Along the bottom are the even numbers. Above each even along the top diagonal is listed the value of 1/2 the even below - primes are denoted by solid dots, non-primes by open dots. Solid blue lines represent values which are not prime addends to the value at the bottom, i.e., sieved values. Each cycle of the output progressively sieves factors so you see 3, then 3 and 5, then 3 and 5 and 7, and so up up to 3,5,7,11,13,17. Each cycle the next prime shows as green then purple then it becomes blue to merge with the previously sieved values.