When Trump made a similar claim in August, we looked at his numbers on criminal undocumented immigrants, finding them to almost certainly be highly inflated. That assessment is below.

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"We are going to stop illegal immigration pouring into our country," Donald Trump told CNN's Anderson Cooper during an interview that aired Thursday night. "My first day in office, I am going to notify law enforcement authorities that all of the bad dudes — and we have a lot of them — that are here illegally, that are the heads of gangs and drug cartels and all sorts of people. …"

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"People who commit crimes," Cooper interjected, according to a transcript from CBS's Sopan Deb.

"And there are probably millions of them, but certainly hundreds of thousands. Big numbers," Trump replied. "They're out. They're out. The police know who they are. I've spoken to many police. The police know who they are. They deal with them all of the time."

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A bit later, Cooper asked if those who hadn't committed crimes would be deported.

"We know the bad ones," Trump replied. "We know where they are, who they are. We know the drug cartel people. We know the gangs and the heads of the gangs and the gang members. Those people are gone. And that's a huge number." He added, "We're going to deport many people, many, many people, the bad ones."

"The vast majority of those 11 million are not criminals," Cooper said.

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"Well," Trump replied, "we don't know that."

Well, we do.

From the first day of his candidacy, Trump has argued for new immigration restrictions on the basis that illegal immigration led to higher crime. The original formulation was his infamous description of Mexican immigrants: "They’re bringing drugs. They’re bringing crime. They’re rapists. And some, I assume, are good people."

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As the days passed and he was asked to defend that position, he reiterated it. "I said tremendous crime is coming across," he explained on Fox News last July. "Everybody knows that’s true. And it’s happening all the time."

The Washington Post has fact-checked the claim multiple times, including in April when Trump said, "People that shouldn’t have been here, people that should’ve never been allowed to come over the border, and they come here like it’s nothing. … You know, I’m looking at statistics where your crime numbers are so crazy, they’re going through the roof, so we can’t have it anymore."

In most cases, our fact checkers have pointed to a report from the nonpartisan Congressional Research Service that looked at this issue. The CRS produced this graph, approximating the small subset of immigrants here illegally who had also committed violent crimes.

Note that this is "roughly to scale," though the CRS couldn't determine what proportion of the violent criminal noncitizens were also here illegally. The vast majority of those arrested for violating federal crimes while here illegally were arrested for being here illegally, according to the most recent data included in the CRS report.

We do know, thanks to Pew Research, that first-generation immigrants (here legally and not) are much less likely to commit crimes than their children — or than native-born Americans.

Supporters of Trump would note that even one crime committed by someone here illegally is too many. That, of course, is true. It's also true that one crime committed by an American citizen is one too many. The question is the accuracy with which how the Republican nominee for the presidency depicts a broad population living in the United States.

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Speaking of: When Cooper pressed Trump on the issue, the Republican nominee introduced another point of fuzziness. Cooper spoke of there being 11 million people here illegally, to which Trump replied, "It could be 30, and it could be five."

This, too, is a throwback to the early days of the campaign, when he said he heard there were 34 million immigrants here illegally, an inaccuracy probably stemming from faulty reporting on a government request for printing new green cards. Pew Research and the Department of Homeland Security put the figure at a little over 11 million — and Pew estimates that it has stayed flat in recent years.

It's worth pointing out that police officers who are aware of criminal activity by "bad dudes" are empowered to arrest the culprits. (A "sanctuary city" is not a place where immigrants here illegally have a blank check to commit crime; rather, those cities are generally ones where undocumented immigrants aren't turned over to the federal government if identified as being here illegally but without having committed another crime.) The heads of violent criminal gangs and drug cartels could — and should — be arrested anyway, and an executive order from the president won't prompt that to happen.

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But more broadly it's worth pointing out how neatly this issue delineates the entire arc of Trump's campaign. The candidate targeted immigrants for criticism even before he said the words, "I am officially running for president of the United States." When his incorrect numbers were pointed out, he stuck by them — and continues to stick by them, to this day.