Washington (CNN) President Donald Trump's Oval Office remarks on Thursday before a meeting with Irish Prime Minister Leo Varadkar were so thoroughly inaccurate it was a challenge to figure out which to fact check first.

We're still looking into some of Trump's claims. But here are the two we picked as most egregious:

Trump falsely claimed anybody coming into the US from Europe is being tested for the coronavirus

When a reporter noted that an American could bring back the coronavirus even with Trump's new travel restrictions on some European countries, Trump said, "Sure. But we have them very heavily tested. If an American is coming back or anybody is coming back, we're testing. We have a tremendous testing set up where people coming in have to be tested."

Facts First: It's not true that Americans or others returning from Europe "have to be" tested for the coronavirus -- and no system is being set up to actually test these returning travelers.