Multiple phone calls claiming to be Xfinity

Yesterday, I received a phone call from [Edited: "Invalid Phone Number"].  The caller ID showed Xfinity so I answered.  The person on the line claimed that he was calling from Xfinity with a deal that could lower my monthly internet bill.  He knew my name and monthly billing amount.  I told him to email me the info and call back later.  I did not reveal any personal info.  In the meantime, I checked out the phone number and saw that it was likely a scam.  I never received an email from Xfinity. 

Later that day, he called back so I told him I never received the email.  He claimed he sent it and said he would resend before I hung up.  I then received an email and text from Xfinity that said "Thank you for reaching out.  Click the button below/ click the link to complete your request".  It looked suspicious so I called Xfinity Customer Service.  They said they did not have any record of reaching out to me, nor of me requesting any additional info so I deleted the email and text without clicking the links. 

Later that evening and this morning, I received over 15 more calls from various numbers: [Edited: "Invalid Phone Number"].  I received 7 calls in 5 minutes from various numbers.  I answered one this morning and the person on the line claimed once again to be Xfinity and was "following up" on my issue that I reported yesterday.  I asked him what issue he was referring to, and he replied that it was the internet issue.  I told him that was not the issue I contacted customer service regarding and hung up.  It concerns me that these people have my contact information and know that I use Xfinity and know how much my monthly bill is.  Also concerned with the aggressiveness and frequency in calling - it's bordering on harassment.  Also the fact that it seems the scammer could access my account somehow to request email and text followup.