It is not only people with private health insurance who receive private prescriptions from their doctor. People with statutory health insurance can also get a private prescription if the drug requires a prescription but is not included in the list of services covered by statutory health insurance.
You will also receive a private prescription when non-prescription medicines are prescribed. You will then have to pay for these yourself. If your doctor is not licensed by the health insurance provider, they will only issue private prescriptions.
Private prescriptions are valid for three months from their issue date.