What is the fastest processor I can put on HP laptop (6710b)?

Your laptop has a Socket P motherboard, meaning it can support Intel's mobile T & P lines, which includes both the 65 (t7-8***) and 45nm (P9***) lines. The fastest you can put in there is the 2.53 gHz 45nm P9500. I should also note that with the 45nm architecture, you can easily overclock that puppy to >3.00 gHz stable, uming you have an unlocked BIOS (which I highly doubt). Otherwise, you'll still benefit from the lower energy use.