I have a landline with Primus and Telus had to clear something with them in order for me to get Telus.

What does Telus highspeed have to do with a landline?

Can I get Telus without a landline? What if I cancel my Primus landline? Will my highspeed still work?

Unlike Rogers, which uses cable to provide internet, Telus (as well as Bell) uses DSL (Digital Subscriber Line) for their internet, which requires an active telephone line to provide the transmission. Whether that is their own line, Bell's, or Primus, it needs to get in somehow...

Telus will sell you DSL internet without an active phone line, so you could cancel Primus but you'd probably want to talk to Telus first. What you're looking for is "Dry Loop DSL" or "Naked DSL" see: http://en.wikipedia.org/wiki/Dryloop_DSL