Even while energetic young people are fleeing the rest of the state, the Big Apple continues to be a big draw, a new report shows.

New York City gained 300,000 new residents between the ages of 20 and 34 between 2000 and 2010, the report by the Empire Center for Public Policy shows.

The influx includes new immigrants from other countries, those who move to the city from other parts of the state — and people who come here with a dream from cities and states around the country, said report co-author E.J. McMahon.

“This is where people still flock to,” he said. “It’s not the only place, but it’s seen as an exciting place to work and start one’s career.”

There are now 1.4 million people between the ages of 25 and 34 living in the city, the report shows.

“New York City is the place to be. It’s a world city,” McMahon said.

Young people are attracted to the colleges and universities and a wide range of professions including law, finance and advertising, McMahon said.

But the U.S. Census numbers reviewed by the Empire Center also show that many of the young people who moved to the city in the 1990s moved out once they reached middle age in the following decade.

It’s why the population of children and teens dropped here between 2000 and 2010.

“New York City is a place young people still want to be, but it’s also a place people don’t stay in when they start their families,” he said. “People come here when they are young and leave when they get older.”

According to the report, 24.4% of city residents are under 19, 24.9% are between 20 and 34 years old, while the rest are 35 and over.

The city population is also aging at a slower rate than the rest of the state and country.

The median age in the city grew from 33.6 in 1990 to 35.5 in 2010 — a jump of 1.9 years.

That’s compared with the rest of the country where the median age was 37.2 in 2010 — 4.3 years older than it was in 1990.

Upstate New York is even older than the rest of the country. The median age across the state was 40 in 2010 — 6.6 years older than in 1990.

It’s a problem that upstate communities should address, the report found.

“A state, region or community that attracts young people — and retains them as they build careers, businesses and families — is in a good position to build for the future,” the report says.

The report calls youth “an especially valuable asset” but one that has been “rapidly depleted in some parts of New York.”

A previous Empire Center report found that New York lost 2.9 million residents to other states between 1990 and 2010, though much of that was offset by a heavy influx of foreign immigrants to New York City.

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