I'm creating this thread to organize the post-mortem analysis of the Running Numbers problem. Please put any new post-mortems here. If you want to go over Maze of Life and Consecutive Primes, please create similar threads in their respective forums.
Several contestants have already put their post-mortems in another thread. I will include them here by reference:
vdave got things started by describing his lookup table to break the 2 SSE instruction barrier.
lazydodo used a static lookup table to see if a potential solution was within the next 36 adds.
smayne's approach involved a mask of unmodified LSB's to see if the next 36 steps could be skipped.
jmfernandez's algorithm selected a candidate byte. He had other pending improvements.
duncanhopkins went with a batch approach, breaking the work up into 512*37 cycle sections.
VoVanx86 described his parity test for skipping 36 cycles ahead.
Let me know if I missed anything and I will edit this post. My own post-mortem will be forthcoming is below.