At the Twitter support page
https://support.twitter.com/articles/20171312# , it says:
4. Enter your phone number. Please note that unless you have otherwise associated a phone number with your account,
we will delete it after verification is complete.
I'm just not sure I believe they'll actually delete it after sending me the code!
I have a TracFone that I keep in my purse for emergencies when I'm out and about. It is connected to my real name at my TracFone website account. But I think I'll use that one. I'm a techno dummy in many ways, but I don't think I can even receive a text message on my house phone, anyway. LOL
Thanks!