http://primes.utm.edu/bios/top20.php show three categories for "the highest sore" :

The Prover-Account Top 20

Persons by: number score normalized score

Programs by: number score normalized score

Projects by: number score normalized score

By score you are going to find it extremely hard to beat GIMPS it's 70-80 thousand computers

So I guses you mean by "number of primes". This is a hard task because you find smaller primes quickly but those primes will be falling out of the top5000 as the tide rises. Reisel Prime Search or PIES is your best bet for "by number of primes" records.

Small k as in "k*2^n-1" are quicker to number crunch -- all relative densities taken into account. The 321 project uses 3 which is quiet dense, ie, lots of candidates (5.75% left after sieving optimally) but with hopefully a greater density of primes. But even so it is quite hard to find them. Maybe you should do a couple of 321 files for the project. You will have to have patience because a single core at 3GHz+ will take ten days. If you find a prime it will be 13th largest in the world ( until it is beaten...). Okay it's not #1. But 321 to GIMPS is as pygmy is to a giant.