BGP routes on Cisco 3750G-12S

Hello all. Long time lurker here. Just have a quick question for those familiar with these switches.

I run 2x Cisco 3750G-12S switches in a DC. I run iBGP between the two switches and have route-reflector clients downstream of them. Upstream I have connectivity from each switch to two transit providers and an intermediary with LINX.

My question is this. I accept a bunch of routes over the ‘intermediary’ peer in order to steer as much traffic towards LINX as possible. These switches only handle around 8K IPv4 and 8K IPv6 prefixes (if I remember correctly!) Currently, I’m taking in just short of 2K IPv4 prefixes on each switch and these are then being exchanged over iBGP as well thereby forming multiple paths to these destinations. Does this in effect use 4K out of the 8K prefix capability or does it only count as 2K prefixes but use slightly extra ram to store the additional paths?

I apologise in advance if this seems like a silly question but I can’t seem to get a clear answer on Google.

Thanks for reading.