The reason for prayer dictates whether it should be kept private or not.  Matthew 18:20 is the perfect example of not keeping it private.  Prayer before a public meeting is not for the individual person. It is to receive God's blessing and guidance on doing His will. Therefore, it's not a thing to be kept private.

Now whether or not you believe in he Christian God is another argument. If you are non-believer in any god, why do you care?