the gateway 503gr uses the intel 915 chipset and you can only upgrade to another pentium 4 500 series processor (no pentium d, no core2duo). you *may* be able to use a p4 600 series cpu but you should contact gateway since intel's 915 mobos only support 500 series and lower p4s: http://support.intel.com/support/motherboards/desktop/d915glvg/sb/CS-026956.htm
since you already have a 3ghz p4, only a 3.4ghz chip could be considered an upgrade. but, the p4 500 series was superseded by the 600 series 2 years ago, and i can't find any retail 500 series cpus. you might take a look at ebay and see what's avaiable.
im trying to upgrade the processor on my gateway 503gr(http://support.gateway.com/s/PC/R/3724/4172nv.shtml) and was wondering what my options are. If anyone could help w/this it'd be greatly appreciated