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The population of the Republic of Ireland stands at an estimated 5.01 million, according to the Irish Central Statistics Office.
It is the first time that the population has risen above five million since the 1851 census when the comparable population was 5.11 million.
It also represents an increase of 2.19 million on the census of 1961.
The CSO said positive net migration and a natural increase meant a population growth of 34,000 in 12 months.
Meanwhile, the population aged 65 and over increased by 22,200 up to April 2021.
There were 742,300 people living in the Republic Ireland aged 65 and over in April, an increase of 17.9% on five years ago.
Statistician James Hegarty told Irish broadcaster RTÉ that the latest statistics reflect some of the demographic and social impacts of Covid-19.
He said migration was one reason why the population had risen.
In 2021, more than 30,000 Irish people returned to live in Ireland, while 22,000 Irish people went to live abroad.
"That's only the third time since 2010 that more Irish have returned than left," he said.
Mr Hegarty said the general population had grown by about 6% since 2016, while there has been an increase of about 18% in those aged over 65.