Tesla Coil Primary Coil Diameter
First of all, you have left out a lot of information. What kind of Tesla coil are you building? A spark gap Tesla coil? A solid-state Tesla coil? A dual resonant solid state Tesla coil? An off-line Tesla coil? 

Chances are your secondary height ratio is wrong. For a spark gap Tesla coil, your height-to-diameter ratio should be no more than 6:1, meaning the height should not be more than 6 times the diameter (in your case, 4 inches * 6 means don't make a secondary any taller than 24 inches).

As for your primary, yes -- 2.5mm diameter wire is much too thin. It will add excessive resistance, creating extra losses in the form of heat and will have poor high-frequency performance. Try to find some 3/8" or 1/2" diameter copper tubing. Many times it comes from a hardware store already coiled up. Without telling us your location, it's difficult to offer possible sources for the materials. 

So, to sum up: Shorten your secondary coil to 24 inches (assuming you're building a SGTC) and definitely find wider primary coil wire or tubing. Otherwise, it's not even worth building a Tesla coil -- It most likely won't work well, if at all.