The United States recorded its 4 millionth confirmed coronavirus case Thursday, a spread that would have been hard to fathom five months ago. Fully a quarter of those cases were recorded in the past 16 days.

To hear President Trump tell it, this is an artificial milestone. The reason we’ve recorded so many cases, he argues, is that we’ve done so many tests. It’s an effort to spin bad news — worst outbreak in the world — into good, highlighting the increase in testing over the past few months. But it’s also thoroughly disingenuous.

“Every time you test, you find a case and it gets reported in the news: We found more cases,” he complained during an interview that aired on Fox News on Wednesday night. “If instead of 50 [million], we did 25, we’d have half the number of cases.”

“So I personally think it’s overrated,” he continued, “but I am totally willing to keep doing it. You know we have so many more tests than any other country by far.”

“I’m okay with it if they want to do it,” he added later, “but again, it makes us look bad, but they say it’s good.”

It is not the case that simply cutting the number of tests would cut the number of cases, as reflected in Washington Post and COVID Tracking Project data. On July 22, the United States conducted just under 800,000 tests, bringing the seven-day average of tests conducted to about 783,000. On May 29, that average was about half as large, just over 390,000. On that day, the seven-day average of new confirmed cases was 20,652. On Thursday, the figure was 66,834 — more than three times as high.

But on April 24, we were conducting about half as many tests as we were by May 29 — and confirming more cases (a seven-day average of 28,779). What’s important isn’t how many tests you conduct but who you’re testing. Early in the pandemic, with limited testing available, states tested a lot of people already showing severe symptoms, driving up the rate of positive results. As testing supplies became more widely available, we could test more people, including more people who weren’t infected.

With the recent surge in new cases, which began in early June, tests were again constrained — in part because of how broadly the virus had spread. Since mid-March, the increase in tests conducted each day has grown steadily, even as the number of confirmed cases has varied.

What’s particularly odd about Trump’s attempt to tie new case totals to the number of tests we’ve completed, though, is that he’s actually right, just not in the way he means. It is the case that doing less testing will detect fewer cases — which we know because we’re conducting too few tests to catch all of the actual infections that have occurred.

In other words, the testing Trump says makes us look bad by measuring the spread of the virus actually makes the United States look better than it should, since so many cases go unrecorded.

This isn’t unique to the coronavirus. Each year, the Centers for Disease Control and Prevention develops an estimate of the actual spread of the seasonal flu, as not every case is positively identified. It did the same with the H1N1 pandemic in 2009.

This week, it published a study suggesting that during the coronavirus pandemic, too, the number of recorded cases was significantly lower than the number of infections. In some areas, the number of unidentified infections could be six to 24 times higher than the recorded total. That finding mirrors a comment made by CDC Director Robert Redfield, who estimated in June that we’ve missed nine cases for every one that’s confirmed.

Data scientist Youyang Gu has been using machine learning to develop estimates of the number of cases that have escaped detection. His data suggest that the number of new infections each day at this point is six times higher than what’s actually being recorded: It’s likely the United States is experiencing about 400,000 new infections instead of about 67,000. His estimates, in fact, suggest that the number of new infections each day over the past few weeks has been higher than at any point in the pandemic.

The difference between the confirmed total and the estimated total is stark.

How are we missing so many cases? In part because many people are infected but not showing symptoms, so they don’t know to be tested. In part because we don’t have a robust contact tracing system that would let us identify people who might fall into that asymptomatic category. And in part because we’re still seeing constraints on testing supplies, which make catching up to the spread of the virus difficult in places where new infections are rampant.

Gu’s model aligns with the CDC’s estimates and statement. Since the number of tests being conducted each day passed 100,000, his model estimates we’ve missed between four and 11 cases for every case we’ve confirmed.

In other words, Trump’s getting precisely what he says he wants: too few tests to actually capture all of the cases that exist. Yes, it’s possible other countries have failed to detect or report new cases at an even greater rate than has the United States. But it’s nonetheless the case that for all of Trump’s complaints, the virus is actually much more widespread here than indicated by the confirmed totals he dislikes so much.