Your queries do not produce the same result. SELECT from x left join y on x.c is an outer join whereas SELECT from x, y where x.c = y.c is an inner join. Ok, it is a cross join, but most databases will transform it to inner join. I would like to know what are those SQL engines which do a cross join when using the select from x, y where x.c = y.c syntax. Even SQLite converts comma joins to inner joins if it is more efficient to do so. Also, using left joins when inner join is the thing you want is not good for performance. You can look the above link for explanation why.

Maybe they need patents from other companies. Making a 3G phone without infringing any other company's patents is near impossible.

The short answer is that there is just too many primes to list. There is about x/log(x) prime numbers smaller than x. If you have a 512 bit number then you have about sqrt(2^512) / log(sqrt(2^512)) numbers to check. So, there is 1.5 * 10^75 numbers you need to list. This is simply impossible. Moore's law will not help here, as adding one bit to the number to check about doubles the search space. That is, after a year of you can check a number that is just one bit larger!

Well, all that a chess program does is that it essentially plays all the possible moves out to some cutoff point. I wouldn't claim it a big success if you don't use probabilistic methods.