In 30 years, the number of Americans covered by Medicare will nearly double to 77 million, or 22 percent of the U.S. population. Beneficiaries born in 1900, who enrolled in Medicare in its first year, 1966, are celebrating their 100th birthday this year.There are families with two generations, parent and child, both of whom are enrolled in Medicare today; some families have three generations enrolled in Medicare.eneficiaries born in 1900, who enrolled in Medicare in its first year, 1966, are celebrating their 100th birthday this year. There are families with two generations, parent and child, both of whom are enrolled in Medicare today; some families have three generations enrolled in Medicare.