(CNN) There are several treatments being studied to prevent or treat coronavirus, but President Trump has been a cheerleader for one in particular: hydroxychloroquine , a drug currently used to treat malaria, lupus and rheumatoid arthritis.

Over the past month, he's made many optimistic statements about hydroxychloroquine. CNN has fact-checked the president multiple times -- such as here here , and here -- and found that he's being unrealistically enthusiastic.

Physicians, including Trump's own advisor, Dr. Anthony Fauci , have emphasized that in order to know if a drug is going to work -- and be safe -- it has to be studied in clinical trials. It might work, but it might not. It might be safe, but it also could hurt patients.

Clinical trials are considered the gold standard in medicine. Boiled down to the essentials, clinical trials take a large group of people, give half of them the drug and half of them a placebo, and see how each group fares.

The half that takes the placebo is called the control group. The reason to have a control group is that it allows the doctors to tell if it's the drug itself that is having an effect on the study subjects, and not something else. If the drug group and the placebo group have the same results, then it's likely the drug did not have an effect.

CNN searched clinicaltrials.gov , the National Institutes of Health database of privately and publicly funded clinical studies around the world, and found there are at least 15 research centers in the United States studying hydroxychloroquine to prevent or treat coronavirus.

Over the past few weeks, Trump has made several erroneous statements relating to hydroxychloroquine studies. Here are basic questions about these studies with answers from the president and then answers from doctors.

Question #1: How soon until we know if hydroxychloroquine works against coronavirus?

Trump says "days."

Doctors say weeks or months.

On March 29 on Fox News, Trump said "we're going to have a good idea over the next three days" whether hydroxychloroquine and azithromycin work. "I think it might be successful ...we're going to know within days."

Azithromycin is an antibiotic better known as Zithromax or a Z-pack.

Of the 15 US research centers, only a few are studying hydroxychloroquine and azithromycin in combination; most are studying just hydroxychloroquine.

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CNN reached out to the 15 centers to ask how long it would take them to get results. Seven centers either did not respond or said they didn't know.

For example, doctors conducting a large clinical trial at Henry Ford are aiming for more than 3,000 participants and say it will take about four months to conduct their study. Researchers running a trial at New York University and the University of Washington say they'll have around 2,000 study subjects and expect to have results in June or July.

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Two centers said they could have results within weeks. The University of Minnesota is doing a study to see if hydroxychloroquine can help prevent people from becoming infected with coronavirus. They say they could have results May 7, or possibly even earlier. (Here's a story about a physician who's a study subject in that trial.)

Rutgers University said they could have initial results by late April or early May on their study of whether hydroxychloroquine alone, or in combination with azithromycin, might help treat coronavirus.

The reason a clinical trial can't be done in days is because the universities need to recruit study subjects, who then need to take the pills for a period of time. Doctors need to analyze the results.

That all takes time -- even when doctors are moving at lightning speed because of the pandemic.

"We need rigorous science, we need the right science," said Dr. Ruanne Barnabas, the principal investigator at the University of Washington. "This is the most urgent study we've ever worked on and we're moving quickly to get results."

Question #2: French researchers have already done a clinical study showing hydroxychloroquine works as a treatment for coronavirus. Doesn't that tell us something?

Trump says yes.

Doctors say the study was terrible, so no.

Trump spoke glowingly about this small French study at an April 5 White House briefing.

"You've seen the same test that I have," he said. "In France, they have a very good test."

He also referred to the study in a March 21 tweet and wrote that hydroxychloroquine plus azithromycin "have a real chance to be one of the biggest game changers in the history of medicine."

But the French study has come under so much fire that the journal that published it is reviewing it again and wrote that "a correction to the scientific record may be considered."

There are several concerns about the paper, including that it ignored patients who took the drug and fared poorly.

Experts described the French study to CNN as "a complete failure" and "pathetic."

Question #3: Have some people tried to delay hydroxychloroquine clinical trials?

Trump says yes, and he came to the rescue.

Doctors say they have no idea what he's talking about.

Trump has said some unnamed force has been trying to keep hydroxychloroquine research in the lab and he's had to swoop in and fight to move it forward into human studies.

"But we don't have time to go and say, 'Gee, let's take a couple of years and test it out. And let's go and test with the test tubes and the laboratories. We don't have time," he said at an April 5 White House briefing

On March 30 he told Fox News that the drug was being studied in people and, "I think that's better than testing in a laboratory, but you know, the doctors tell me no. Some doctors tell me no," he said. "And I got it done because I said, look, some of these people are very sick and they're not going to make it. Let's do it. Let's get it done."

Trump offered no proof that anyone was encouraging that hydroxychloroquine be tested in a lab, much less for "a couple of years."

The infectious disease experts interviewed for this story, told CNN they don't know of anyone who advocated for hydroxychloroquine research to be slowed down -- in fact, they were planning their hydroxychloroquine trials before Trump ever mentioned the drug.

Trump first mentioned hydroxychloroquine on March 19 at a White House briefing.

Dr. David Boulware, who's running the University of Minnesota trial, says he started planning his study ten days before that, on March 9.

By March 18, the day before Trump first uttered the word "hydroxychloroquine" in public, Boulware had already recruited 61 study subjects, according to his research website.

In days, Boulware accomplished what he says usually takes more than a year to do.

"For clinical trials, this has by far been the fastest of my career," he said. "I think it's broken world records."

Question #4: Is hydroxychloroquine safe for coronavirus patients?

Trump says yes.

Doctors say the drug can have serious side effects.

Trump makes it sound like hydroxychloroquine is harmless.

"It doesn't kill you," he said at a briefing on April 1, one of just many times he's repeated that sentiment.

"What do you have to lose? Take it," he said at an April 4 briefing.

The label for Plaquenil, a brand of hydroxychloroquine, says patients taking the drug have reported "life threatening and fatal" cardiac problems and "irreversible" vision problems.

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