Rand Paul has repeatedly touted that he is the only Republican running for president who beats Hillary Clinton in several polls in key states.

"When you poll me against Hillary Clinton, we lead her among independents in five of the battleground states," Paul told Wolf Blitzer on Thursday. The senator from Kentucky has been making claims like since as early as March and made them as recently as last week, when he told Boston Herald Radio that he led Clinton not just among independents, but outright, in "five states that were previously won by President Obama."

Paul, who has not said which states he is referring to, has indeed defeated Clinton in certain head-to-head polls in states that Obama won in 2012 that could be regarded as swing states. But Real Clear Politics shows that no such poll has been taken in months, as Paul has faded from the ranks of the leading contenders for the GOP nomination.

According to Real Clear Politics, the last time Paul beat Clinton in a head-to-head poll in a state Obama won was taken in late July in New Hampshire, when he won by two points. By the same token, the last time Paul was ahead of Clinton in a poll in Pennsylvania was June, which was also the last time a poll showed him winning against her in Ohio. In Iowa, the last poll in which Paul surpassed Clinton was taken in April. The same poll is the most recent time the two were pitted against each other in Colorado, and showed Paul ahead by three points there.

Paul could also have been talking about North Carolina, which Obama won in 2008 but Mitt Romney won in 2012, and where a July poll showed him ahead of Clinton by one point.

The most recent head-to-head poll between Paul and Clinton in any of these six states was taken between August 21 and August 24 in New Hampshire by Public Policy Polling. It showed Clinton up by ten.

The Rand Paul campaign did not reply to a request for comment.

Paul often argues that pollsters are pushing undecided voters to make a choice they haven't really made, that the number of people polled is too small a sample, or that, because polls have margins of error, his real level of support could be much higher than they suggest.