Five. And you'll need to do more than scale them for party size. A number of them need considerable beefing up. Best early example: Macbannin in adventure #2. (Fights in Zeitgeist are often one-offs, so the players usually tackle them at more-or-less full strength, which turns dailies into encounter powers!)
To add to what gideon said: I strongly recommend thinking about introducing healing surge costs into skill challenges to try and strain player resources a bit more, because otherwise the amount of battle healing in 4e can be overwhelming. Maybe not from the first session, but as soon as you get a hang on general group dynamics.
I started with a party of 5, but lost a player fairly soon after starting. I have been running the adventures as written quite successfully with only 4 players. I imagine that 6 players will require a bit of tweaking.
Zeitgeist 4e is generally on the very easy side, and can be completely stomped by any group with even a modicum of mid-op characters. Not even high-op, but mid-op. Our group played through books #1 through #8 with three mid-op PCs, and books #9 through #13 with two mid-OP PCs. Despite the DM actually beefing up encounters, we have still been completely crushing them, especially at the epic tier.
The only real difficulties stem from monsters with inexplicably potent one-off mechanics, like Reed Macbannin's curse of the writhing cauldron, or Lya Jierre's sunder, or the various forms of antimagic.
Zeitgeist for Pathfinder 1e is even easier. The monsters and NPCs there are very weak.