This person with a private number has been calling you from time to time but when you try to pick the call, they turn taciturn and sometimes hangs up the call. 

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You get so annoyed and start thinking of how to block and prevent them from reaching out to you.  Many people have been trying to figure it out, without any success. 

It is possible to block that person.

For android users, depending on your phone manufacturer, there are varied steps to take. On the phone app, tap more then proceed to Call Settings, under it click Call Rejection. 

You will then tap 'Auto reject lists' and then click the 'Unknown' option and calls from that anonymous person will be blocked. 

If you find it hard to block them with the above procedure, download an application dubbed Extreme Call Blocker and you will be good to go.

For iPhone users, go to settings,  turn 'Do Nor Disturb on Manual' and select only to allow calls from your contact list. You can also block repeated calls from the same unknown number.