This undated file image shows the main gate of the Nazi concentration camp Auschwitz I near Oswiecim, Poland, which was liberated by the Russians in January 1945. Writing at the gate reads: “Arbeit macht frei” (“Work makes you free). (AP)

They terrorized Europe for more than a decade.

They exterminated six million Jews.

Their empire ended in 1945 — before NATO, before Israel and even before the bombing of Hiroshima.

Yet even in the age of Obama, those who helped the Third Reich wage a world war keep popping up in unexpected places. One who allegedly served at Auschwitz was arrested in Northeast Philadelphia in June. And this week, Oskar Groening, 93, was charged in Germany with 300,000 counts of accessory to murder for helping guard the notorious death camp. Though Groening, the IB Times reported, denies committing crimes, he hasn’t been shy about discussing the horrors of Auschwitz. “I saw another SS soldier grab the baby the legs,” he told Der Spiegel in 2005. “He smashed the baby’s head against the iron side of a truck until it was silent.”

This genocide and those who perpetrated it have haunted history for generations. When will the last Nazi war criminal finally shuffle off this mortal coil?

Of course, there is no way to know. People die without reference to life-expectancy trends. And many Nazis remain unidentified, at large or in hiding — especially after recent legal changes in Germany made it easier than ever before to arrest and prosecute Nazi war criminals. Rabbi Marvin Hier, the founder of the Simon Wiesenthal Center, estimated last year there might be hundreds still living in the United States

I would have said thousands,” he told New York magazine, “but they’re in their eighties and nineties, and many of them may have died. So it’s very hard to give you an exact figure.” 

But there is a way to guess.

First question: How old did someone have to be to commit a war crime in Nazi Germany? After all, soldiers younger than 18 served the Third Reich, including members of the Hitlerjugend, or Hitler Youth. Some members of the SS 12th Panzer Division Hitlerjugend, who assassinated more than 150 Canadian prisoners of war in 1944, were born in 1926, making them about that age, and German prosecutors have sought to charge other criminals that young. But 16 seems a better cutoff — a 16-year-old war criminal tried by a U.S. military tribunal at Dachau for the murders of three American airmen would have been born around 1928.

With Nazi-hunting entering its seventh decade, the age of those being hunted is a major factor.

You have to take into account that at least many tens of thousands or even hundreds of thousands of men (and some women) were participants in these crimes at a relatively young age,” Efraim Zuroff, the director of the Simon Wiesenthal Center’s Israel office, told New York magazine last year. “And that thanks to the progress of modern medicine, many live today to age 90 and above.”

But how long do Germans live on average? German records before the end of World War II aren’t reliable, but one researcher from Erasmus Medical Center in the Netherlands pointed out last year that life expectancy rose greatly in Europe during the 1920s despite the rise of fascism. The result? German men born around 1928 likely have a life expectancy of about 53 years, and German women born that year can expect to live longer. This means the last Nazi war criminal could have expected to die in 1981 — so Groening and other geriatric alleged Nazis are outliers.

Then again, some Germans live well-past 100. Augusta Holtz, who died in 1986 at 115, was once known as the world’s oldest person (though, for the record, she lacked a birth certificate).

So if a German war criminal — one even younger than the relatively young alleged Auschwitz guards targeted by German prosecutors last year — somehow breaks Holtz’s record, we’ll be hunting Nazis until 2043 and beyond.

Unless that Nazi is, say, of another nationality with a longer life expectancy — such as Dutch, as Dutch life expectancy for those born in 1928 is about 10 years longer.

Certainly, there’s no lack of interest in bringing war criminals to justice, even 70 years after their heinous acts. If anything, approaching death makes the hunt more urgent.

As German prosecutor Kurt Schrimm told reporters last year: “The biggest enemy is time.”