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“Is there a tax write-off thing for cults or is that just religions?” asks Jaime Meline AKA El-P, as he sits in a practise room on LA’s Sunset Boulevard, where Run The Jewels are preparing for their forthcoming world tour. The firebrand rap duo of El-P and Killer Mike have built up a cultish following by adopting the tactics of old-time preachers, touring incessantly while giving their music away for free. Indeed, they unexpectedly brought their new album forward and dropped it on Christmas Eve, where it was downloaded 125,000 times from their website alone, by people supposed to be observing other traditional rituals. But now, El-P has ideas about what a real Run The Jewels cult would be like.

“It’s a very small cult,” qualifies El-P, “and we don’t have any tenets, no ideas about anything; we’re just going for the tax write-off. There’s only a few cults that have managed that transfer from cult status to religious status, and it’s all on some tax-break shit.”

“The big three religions have done pretty good,” adds Mike.

“The big three are killing the game,” says El-P, “and the people.”

It’s an exchange that does a nice job of summing up Run The Jewels: nonsensical musing veering into a sharp critique of organised religion and politics, delivered with comedy timing that Abbott and Costello would be proud of. This mix of serious and silly has proved wildly successful. Since 2013, Run The Jewels have managed to attract millions of believers to their world, where lyrical flow is king, beats are of the chest-pumping variety, and an absurdist ab-libbed joke is only ever a moment away. One minute they’ll be releasing a remix album where instrumentals are replaced with cat noises; the next a protest track about hitting back at police brutality. Their festive gift and third album, Run The Jewels 3, which the pair describe as “harder, darker and angrier” is the latest item off a production line that hasn’t stopped rolling.

“We’re in sync so much now, after two records and several tours – and this new one felt like we hit that point in the Rocky training montage when he’s just killing shit,” says El-P. “We hit the point where we are catching the chicken.”

Chickens, world tours, cartoon versions of themselves in Marvel comics like Deadpool and Howard The Duck, an appearance in video game Gears Of War 4, self-released critically acclaimed albums. You name it, El-P and Mike seem to be able to catch it. Run The Jewels 3 builds on their popularity as larger-than-life foghorns for the good fight. Recorded in rural seclusion in upstate New York, and produced by El-P, it balances the abrasive cuts of rap braggadocio of their previous two albums with more reflective moments, such as anti-hate anthem 2100, alongside Trump takedowns (“Went to war with the Devil and Shaytan/ He wore a bad toupee and a spray tan,” raps Mike on Talk To Me). The album’s guests are a curveball mix, too – certainly not your usual starry rap features. Among them are Detroit motormouth Danny Brown; TV On The Radio’s Tunde Adebimpe; and avant-jazzer Kamasi Washington, who adds evocative sax to another down-beater, Thursday In The Danger Room. Pretty good for a project which started as an experiment.

“There was not a plan,” confesses El-P. “I don’t think there really ever was to be honest. I don’t think we’re a ‘plan’ type of group. We just say yes because it’s fun. That’s always been the guiding principle. It’s got way bigger than we ever thought it would, straight up.” Suddenly the reasons for releasing their album as a free download over Christmas begin to make more sense…

Facebook Twitter Pinterest Run The Jewels, AKA Killer Mike and El-P. Photograph: Steve Schofield/The Guardian

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There’s a strange alchemy in Run The Jewels’ union of cynical New Yorker and gregarious Atlantan. When they first started out, the combination of a ginger American of Irish (and Jewish, Cajun and Lithuanian) heritage and an African-American from the south did draw attention. “You could see guys almost trying to beat around the bush,” says El-P. “We were like: ‘It’s OK, you can ask: how is it possible you guys are not the same race but you’re friends?’ But it’s not crazy for us. It’s how I grew up. This is not my new experience. I did not just make my first friend from outside my direct culture.”

Mike has a simpler take: “I prayed for a brother as a kid and God has brought me one.” That touch of sincerity is taken as an invitation by El-P to fire up another gag. “I wanted a Redline BMX. I never asked for you.”

Mike pauses, before his deapan response. “That’s what you prayed for? You could have just stole that.”

El-P: “Bikes were a little too hard for me.”

Whether or not providence was at play with the forming of RTJ, the project came at a good time for both of them. El-P had been burned by his experiences in the industry, first as part of Rawkus Records act Company Flow who, after critical success in the mid-90s, split from their label and then split up themselves. As a result, in 1999, he co-founded independent hip-hop label Def Jux. It gave the world terrific records by the likes of Aesop Rock and Cannibal Ox, as well as his own successful solo material, setting the bar for underground rap, but it sucked money out of him. Killer Mike, meanwhile, worked his way up through Atlanta’s hip-hop scene, making his name as a featured artist on OutKast’s classic Stankonia album. Buoyed by that success, he signed a solo deal but it left him feeling isolated.

Facebook Twitter Pinterest Killer Mike addresses a rally for Bernie Sanders in Atlanta, Georgia, in February 2016. Photograph: Prince Williams/WireImage

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“Rap to me is communal. It’s something you do with your friends,” says Mike. “So becoming a member of a group was the dream. For me, Coachella and stuff are the highlights, but being in the group is nirvana for me. It is heaven, being able to experience a transfer of energy with [El-P] and the audience.”

Clearly teaming up as Run The Jewels has energised these rap veterans (both El-P and Mike are now 41), allowing them to commune with a new generation of music fans. Mike in particular has made the most of this new platform, and many of those fans have found Run The Jewels via Killer Mike’s outspoken political views. During the spate of police shootings of unarmed black men in the US during 2015, he became a lightning rod for people looking to understand the situation. The powerful speech he made before a gig in a St Louis on the day that the Ferguson grand jury acquitted Michael Brown’s killer went viral, with Mike almost breaking down on stage as he talked about his own children.

More recently, Mike was one of Bernie Sanders’s most high-profile advocates during the Democratic primary race, backing him because of his long-standing commitment to social justice. He appeared on major US talkshows, ostensibly to support Sanders, but at times found himself having to explain things like why his name doesn’t mean he’s actually killed people and why hip-hop isn’t synonymous with crime. It made Mike one of the most identifiable faces of the election, but constantly having to defend himself and hip-hop culture took its toll.

Facebook Twitter Pinterest Killer Mike and El-P photographed in Los Angeles. Photograph: Steve Schofield/The Guardian

“It hurts, to be honest, because you’re an artist,” he says. “You want the world to get it and you’re pretty sure at a certain point that they have got it. So some of that is chosen ignorance and that hurts because I think this artform has done some beautiful things.”

Perhaps understandably then, politics isn’t something the group really want to talk about today. When the US election is brought up, there’s a stoney silence. “Let’s not get into it,” says El-P. “Everyone knows ad nauseum what the perspectives on that are right now. I’m personally fucking tired of the conversation. Y’all got what you want, well, all right – let’s try and make this shit fucking work. It’s going to be horrible.”

The reticence to discuss politics might be down to the hot water that Mike has gotten into by sticking his head above the parapet. When speaking at a college about why he thought Sanders should win the Democratic nomination over Hillary Clinton, and referencing debate at the time over whether women should vote for women, he quoted from a conversation with feminist academic Jane Elliott, who told him: “A uterus doesn’t qualify you to be president of the United States.” Taken out of context, that quote became attached to Mike himself, prompting accusations of sexism.

Facebook Twitter Pinterest Run The Jewels make a guest appearance on Portlandia. How Guardian Guide is that?

Today Mike seems determined to make it clear he’s not a polished political performer, just someone who is tired of things not working the way they should. “I’m not the goddamn ‘marathon for peace’ celebrity,” he says. “I’m the ‘work out your shit, fix your shit, be a whole community and keep on pushing’ celebrity.” This manifests itself in Mike’s charity work and with his commitment to providing off-kilter ideas for how communities can become self-sufficient, like getting into the legal marijuana industry.

Mike’s tell-it-as-it-is honesty is something El-P keeps a brotherly eye on. “Don’t let me do no stupid shit,” Mike says to El-P. “Sometimes I’ll call Mike and be like: ‘Dude, think about this.’” confirms El-P. But Mike’s off-the-cuff approach is a part of the pair’s appeal. Whether live or on a late-night chatshow, RTJ will call bullshit on anyone, regardless of political affiliations.

“That’s why I like Run The Jewels, man,” says El-P, gearing up another surreal metaphor. “It’s like you’ve taken two savage kittens, put them in a sack and thrown them in a river. Each may not be there for the same reason, but they both have the same job: get out of that fucking bag.”

Run The Jewels 3 is out now via runthejewels.com and as a physical release from Friday