Called at 9:29am & 5:17pm. Don't answer unfamiliar calls. Left no message, probably junk.

Been calling every day for more than a week, different times of the day, never leaves a message.

Calling several times a day for several weeks.  Never leaves a message.  If you try to call back you reach no one...no machine, etc.  Yesterday I answered and the person said they were using the internet to call and that my insurance representative had outsourced my number to them to follow up to find out if I was happy with my insurance plan.  If this is true, it is a big problem with my insurance broker.

It sounds like your insurance broker might have a large client list and hired help to make sure their clients are ok.  I would only be concerned if they asked for information

Keep calling, any time of day. I've never answered and they never leave a message. Probably an automated number trying to see if numbers are in use so they can inundate you with spam calls.