@dougmerritt
I ran out of characters to tag you but I was waiting for this <3
As you know, Winograd's algorithm is only/especially interesting for small primes. To my knowledge one would never go past fifty, and The Usual Winograd's algorithm generations don't go above the 20s, if I recall correctly (you probably recall better).
Anyway, there turn out to be lots of numbers that are multiples of three as well as two, in the first place. Infinitely many ;p