In President Donald Trump’s world, the election that he won was rigged. Shortly after he won the 2016 election, Trump claimed on Twitter that “millions of people … voted illegally” on Election Day, costing him the popular vote despite his Electoral College victory. On Monday, he doubled down on those remarks in a closed-door meeting with congressional lawmaker. And on Tuesday, his press secretary said that Trump’s beliefs about voter fraud are based on “studies and evidence.”

Do studies actually support what Trump is saying? Are millions of Americans really voting illegally?

The answer is, simply, no.

Part of that is because the study Trump and his team have repeatedly cited — from the Pew Center on the States — couldn’t even begin to prove what Trump alleges. The 2012 report isn’t even about voter fraud; it’s about the technical aspects of voter registration systems, and how America could save money by upgrading how it registers voters.

In fact, David Becker, who worked on the 2012 report, has spoken out against Trump’s claims.

As I've noted before, voting integrity better in this election than ever before. Zero evidence of fraud. https://t.co/BBS8NVcACB — David Becker (@beckerdavidj) January 24, 2017

But there’s a reason Trump and his team can only seem to point to this report to back up their claims: When you look at analyses that have focused on voter fraud, they find it’s simply not widespread or even a little common.

What the Pew report actually found

In 2012, Pew conducted an investigation into how US voters are registered. The report, titled “Inaccurate, Costly, and Inefficient,” found that approximately 24 million — one of eight — voter registrations in the US are no longer valid or significantly inaccurate. And more than 1.8 million registered voters were actually dead, while 2.75 million had registrations in more than one state. This is where Trump apparently got his “millions” figure.

But, contrary to what Trump and others have suggested, this does not mean that all of these registered voters actually voted. America has a multi-step system for voting: You register, then vote. The report only shows that people registered and were never taken off the rolls. They didn’t even have to register for the latest election — some of them registered for the 2008 election, died, and states just didn’t take them off their rolls.

Pew’s report also doesn’t cite its figures to argue that there’s widespread voter fraud, but instead to show evidence of America’s outdated voter registration system — one that still heavily relied on old-fashioned paperwork instead of electronic or online technologies.

This can be costly, Pew found: “A study Pew conducted with Oregon found that, in 2008, state and local taxpayers spent $4.11 per active voter to process registrations and maintain a voter list, or $7.67 per transaction (new or updated registrations).” In comparison, “Canada, which uses modern technology to register people as well as data-matching techniques common in the private sector, spends less than 35 cents per voter to process registrations, and 93 percent of its eligible population is registered.”

So this is about the cost of outdated voter registration systems — a fairly banal finding — not voter fraud. The report goes on to make some recommendations to upgrade the system (like moving beyond paper-based systems), with a follow-up in 2016 praising some of the progress that some states made since 2012.

Meanwhile, there are studies that look at voter fraud and how common it is. Only they don’t at all back up what Trump has claimed.

Studies that have looked at voter fraud haven’t found much of it

There have been multiple investigations into voter fraud. None of them have found serious evidence of anything close to millions of people voting illegally.

One analysis focused just on voter impersonation, the type of fraud that strict voter ID laws (which Trump supports) aim to curtail. Tracking allegations of this type of fraud, Loyola Law School professor Justin Levitt found 35 total credible accusations between 2000 and 2014, constituting a few hundred ballots at most, when more than 800 million ballots were cast in national general elections and hundreds of millions more were cast in primary, municipal, special, and other elections.

A 2012 investigation by the News21 journalism project looked at all kinds of voter fraud, including voter impersonation, people voting twice, vote buying, absentee fraud, and voter intimidation. It confirmed that voter impersonation was extremely rare, with just 10 credible cases.

But the other types of fraud weren’t common either: In total, the project uncovered 2,068 alleged election fraud cases since 2000, covering a time span when more than 620 million votes were cast in national general elections alone. That represents about 0.000003 alleged cases of fraud for every vote cast, and 344 fraud cases per national general election, in each of which between 80 and 130 million people voted. That’s a drop in the bucket.

What’s more, not all of these — maybe not even half of these — alleged fraud cases were credible, News21 found: “Of reported election-fraud allegations in the database whose resolution could be determined, 46 percent resulted in acquittals, dropped charges or decisions not to bring charges.”

Putting all of this together, the evidence is clear: Voter fraud is extremely rare. It doesn’t add up to the millions in one election, as Trump claimed. In fact, it doesn’t even add up to the thousands in a single election. So Trump may just have to come to terms with the fact he lost the popular vote fair and square.

Watch: It’s now on America’s institutions — and Republicans — to check Donald Trump