By Anna-Catherine Brigida and Maximilian Heath

BUENOS AIRES Argentina's presidential election race has an unpredictable X factor: Javier Milei, a fiery and wild-haired libertarian who wears leather jackets, belts out rock songs to his supporters, and wants to purge politics of what he calls "thieves."

The 52-year-old economist, whose brash showmanship has shades of former U.S. president Donald Trump or Italy's Beppe Grillo, has shot from relative obscurity a few years ago to now polling at one-fifth of the likely vote, with his combative, rock-style rallies appealing to voters angry at 116% inflation and rising poverty.

He has pledged to "blow up" the political status quo, shutter the central bank, dollarize the economy, and massively shrink the state - ideas that have resonated with many voters, especially the young, after years of economic decline.

"Milei is a phenomenon," said Benjamin Gedan, director of the Latin America and Argentina programs at Washington-based think-tank the Wilson Center, adding that his rise had rattled the two main political blocs.

"His plague-on-both-your-houses message resonates among voters fed up with traditional political parties. And there are legions of these voters."

Milei remains a long-shot to win the Oct. 22 general election, but has turned it into a three-way race, challenging the ruling Peronist coalition and the main conservative opposition grouping Together for Change.

He is not facing an internal challenge in this Sunday's primary vote and just needs to reach 1.5% to progress to the October contest. But the result will give an indication of how deep his popularity is and how much of a threat he may be in the general election.

Pollsters peg him at near 20% of the likely vote, a level of support that could give his party significant sway in Congress and him the role of king-maker in an eventual run-off between the two top candidates.

In his closing campaign event this week, Milei rocked into an arena, singing and surrounded by cheering fans. He railed against the political elite who he called "robbers" taking money out of voters' pockets.

"We are coming to defend against the looters of this system, which only benefits the political thieves," he shouted at the joyful crowd as they chanted "freedom, freedom," a reference to his party's name La Libertad Avanza.

A former small-time rock musician and athlete, Milei opposes abortion and supports gun rights. He has criticized worker-friendly labor laws as a "cancer," said the state is the "basis of all problems," and praised U.S. gangster Al Capone as a hero.

Milei's rise reflects a wider regional trend in recent years that has seen Latin American politicians outside the mainstream and pledging to break up the status quo gain prominence in Brazil, Colombia, Peru and Chile.

"People are fed up with politicians," said Adriano Gabriel Zoccola, a 31-year-old lawyer from Buenos Aires who supports Milei because of his economic proposals and plans to slash government spending and cut the number of ministries.

"If Argentina is going to have real change, something completely different has to emerge. I think that Javier is the right person," added Zoccola, who said he had previously voted for Together for Change.

Opponents say Milei's proposals are unrealistic. That includes the plan to dollarize the economy, something most Argentines oppose despite rapid depreciation of the peso currency and high inflation. A dollar-peso peg introduced for similar reasons in the 1990s brought short-term benefits but ended in an ugly devaluation.

Diana Mondino, an economist and adviser to Milei who is running for Congress for his party, said his reputation for being unyielding was the reason many people didn't like him but was also the very thing that made him successful.

"He's not willing to negotiate," said Mondino. "He's willing to say: 'What do we need to get things done?' It might hurt, but it will get done."

Gedan said Milei could pull off a shock result in the election, at the very least shaking up the political panorama.

"In recent elections in Argentina, the two major coalitions gobbled up almost all votes. Now, one-in-five voters will likely vote for Milei - and he could do even better," Gedan said.

(Reporting by Anna-Catherine Brigida and Maximilian Heath; Editing by Adam Jourdan and Rosalba O'Brien)