This company calls several times a day. I can't tell whether they are trying to sell me something or collect a debt. In any case they are incredibly irritating.

I had better win a prize.

harassed

They were probably hired by a magazine company to renew your magazine subscription.  They get paid by how successful they are.  This company may also be phishing for information on "prospective consumers."

According to the Federal Trade Commission (ftc.gov):
If you ask a telemarketer to put your number on their "Do Not Call" list, they MUST do so--even if you have/had a business relationship with the company who hired them to call you.  If the telemarketer keeps hanging up before you can tell them this, call the company who hired them, and tell them you're being harassed and want your number put on their "Do Not Call" list.

Recieved harrasing phone calls from caller at Ebsco Teleservice 3330-429-2913.

Harrasing Phone Calls

Claimed EBSCO subscriptions  wanted credit card data