Max number of TCP connections to one IP?

Is there any limit, imposed by the TCP protocol, to the number of active connections to one IP address on one interface?
I'm asking this because it's easy to add more servers behind a load balancer, but I wonder if the TCP protocol limits in some fundamental way the number of connections to the load balancer itself.
Let's say there's an ACE 4710 load balancer in front of a bunch of Web servers. The balancer exposes one IP address to the clients on the public network. The connections are forwarded to the Web servers on the private network. The balancer is also doing NAT: the servers see the connections originating on a private IP on the load balancer.
On the client side, each connection is uniquely identified by the quartet (source IP, source port, dest IP, dest port). So as long as each client only creates one connection, I think the limit here is just the amount of RAM on the load balancer.
On the server side, same thing, each connection is identified by the same quartet, so I guess the theoretical limit here is 64k connections per server, due to the limit imposed by the source port numbers on the load balancer.
OTOH, if the load balancer is not doing NAT (the servers see the connections originating on the public IPs of the clients), then there should be no limit imposed by the TCP protocol.
Is that right? Comments?

you got it right.
Gilles.

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