Originally posted by vjs
Sieve speed – The speed of the client reported in kp/s, ie 500 kp/s, means that 500,000 p’s are tested against the entire dat file in one second.

p’s – These are prime numbers which are checked against the k/n pairs to see if they are factors for those k/n pairs. If it’s a factor that k/n cannot be prime, a prime has no factors but can be a factor of a larger number.
Just a little correction:

p's in the speed-sense are just plain numbers (which hopefully are factors). The high performance we experience now is partly due to the fact that non-prime numbers can be left out (omitting all even numbers double the speed and so on).

So although only primes are tested for trial factoring, the speed is metered just in numbers...