2000 f4 cuts out while riding
 

I just bought a 2000 cbr600f4.. i was riding first night for around 40 mins and all sudden engine cuts.. after about ten minutes struggled to start back up but then ran again.. did it a few more times but is always coming back on im worried about it not coming back on one time.. any ideas??

One of the common issues with this particular bike is that the stock charging system stops working after it heats up, and as the battery drains, especially if you're in stop and go traffic in hot weather, the charging system can't keep the bike running. After it cools off, it starts up again, until it heats up. This sounds like it could be your problem. Search for threads regarding regulator/rectifier.

Fuel pump
 

Had a similar issue with my f4 it would cut out when getting hot and then start when cooks. I replaced fuel pump then it worked okay.

I had the same issue. It was when i really gave it a lot of throthle for 10-20 minutes. Then short after it would die and i wouldnt be able to start it for some time and most of time i managed to drain my battery first.
After i changed my fuel filter i havnt had this issue! So try that before changing ur fuel pump. My filter was old, used and really dirty.