White House press secretary Sarah Sanders was direct when arguing to Fox News’s Chris Wallace on Sunday that a wall was needed on the border with Mexico to prevent terrorists from entering the country.

“We know that roughly, nearly 4,000 known or suspected terrorists come into our country illegally,” Sanders said, “and we know that our most vulnerable point of entry is at our southern border.”

Wallace pushed back: Wasn’t that 4,000 figure including people detained at airports? Well, sure, Sanders admitted, but the southwest border was still the most vulnerable point.

At least politically. President Trump’s insistence that funding be blocked for several government departments until Congress funds a wall on the U.S.-Mexico border has given new urgency to the administration’s claims about a dire situation in the region — including presenting as accurate numbers like that one about 4,000 terrorists. In fact, as the administration knew months ago and as NBC News reported Monday, the actual number is far lower than 4,000.

We can start with the fact that the 4,000 figure is rounded up. The Department of Homeland Security actually indicates that 3,755 known or suspected terrorists were prevented from entering or traveling to the United States in fiscal year 2017 (which stretched from October 2016 through September 2017).

There are multiple caveats baked into that description itself: Prevented from traveling to the United States means, for example, that people on the terrorist watch list might have bought a ticket to fly here but were not allowed to do so. And that we’re relying on the terrorist watch list should itself be eyebrow-raising: As we’ve reported before, the classified list is sweeping in its scope, and any number of people with no links to terrorism are likely included. (“Who are these people who are so dangerous that we can’t let them on planes, but we haven’t gone out and arrested them?” one expert put it when we spoke in 2015.)

So what part of those 3,755 were blocked at the border? Well, in the first half of the next fiscal year, from October 2017 through March 2018, 132 — including both the borders with Canada and Mexico.

In fact, only 41 were stopped at the border with Mexico, according to NBC’s reporting.

And of those, only six were non-U. S. citizens or permanent residents, meaning that they were the sorts of nefarious international actors implied by Sanders’s rhetoric. Nearly seven times as many noncitizens were stopped at the border with Canada.

But even then, we don’t know how many of those who were stopped were stopped while trying to cross the border illegally. After all, most people who cross either border do so through designated border crossing points, called ports of entry. According to NBC, only five people on the terrorist watch list were stopped between ports of entry by Border Patrol agents in the first six months of fiscal year 2018, though it’s not clear if they were stopped on our northern or southern border.

So that’s six people stopped on the border with Mexico and maybe another five stopped between ports of entry who might have their names on a list meaning that they might have some nebulous ties to terrorism.

In 2017, Trump’s State Department offered a different number as a total of how many established terrorists had entered the United States from Mexico.

There is “no credible information that any member of a terrorist group has traveled through Mexico to gain access to the United States,” a report from the department said.

But let’s assume that these six people were actual international terrorists detained at the border (an assumption that is undercut severely by the fact that an administration happy to trumpet anecdotal evidence of its claims has not paraded them on television). How does that compare to the border on the whole?

Well, PolitiFact estimated in 2016 that there were about half a million border crossings from Mexico into the United States every day, meaning a total of more than 182 million annually. The Department of Homeland Security identifies how many crossings are halted in its annual data. People prevented from entering at ports of entry are deemed inadmissible; in 2018, there were 124,511 such incidents. Those arrested crossing the border between ports of entry — the sort of entry Trump’s wall is meant to prevent — are listed as apprehensions, and in fiscal year 2018, that happened nearly 400,000 times.

Those are big numbers, but they pale in comparison to the overall traffic.

Of those who are apprehended or deemed inadmissible, about a fifth made claims of asylum upon arriving in the United States.

This is a major reason migrants try to cross the border. Those fleeing violence in Central America present themselves to U.S. officials once on American soil and begin a lengthy and backlogged process to try to gain long-term residency through the asylum process. Such claims must be made on American soil, so, experts tell us, some large percentage of those who cross illegally between ports of entry do so specifically to seek out authorities and claim asylum.

In other words, this is not necessarily the image of illegal border crossings that the administration presents.

Nor is this: Of those who were apprehended entering illegally, nearly 4 in 10 were members of families or children arriving at the border by themselves.

This surge in families arriving at the border is what prompted the administration to implement its policy of family separations last year, hoping to dissuade people from making the trip north with kids out of fear of having the children taken away. That policy doesn’t seem to have had much deterrent effect.

The administration offers other numbers, too. It points to at least 17,000 people detained at the U.S.-Mexico border who had criminal records. In speaking with The Post last week, though, a DHS spokesman estimated that most of those detentions were at ports of entry.

The department also released a figure about gangs as part of its sales pitch to Congress on Friday. Six thousand gang members, it said, had been “apprehended at the Southern Border and removed by ICE.”

That “and” is bearing a heavy load. It’s not 6,000 gang members apprehended at the border who were then carted off by Immigration and Customs Enforcement. Instead, the 6,000 gang members figure includes both people stopped at the border and gang members arrested elsewhere in the United States and deported.

How many gang members were stopped at the border? A bit over 1,000, of whom about 200 were stopped at ports of entry.

So not 6,000 gang members busted crossing the border where a wall should be, but only a bit over 800.

Let’s again take a step back. We’ve now determined that there were 17,000 criminals stopped at the border (though how many were caught crossing illegally isn’t clear). We have about 800 gang members crossing between ports of entry. We have six or maybe 11 terrorist-watchlist designees stopped there as well.

How does that compare to our big chart of annual crossings?

Even setting aside the qualifications that apply to those numbers -- that they may not represent people attempting to cross between ports of entry, for example -- it’s not overwhelming.