Phyre Hawkins, Mark Evans, Christopher John O’Neill in the first national tour of “The Book of Mormon,” which opens July 9 at the Kennedy Center. (Joan Marcus)

The box office miracles of “The Book of Mormon,” chapter and verse:

The musical has played to over 100 percent capacity audiences on Broadway since opening more than two years ago. Thanks to demand, its average ticket costs nearly $200. That’s highest on the strip, as is its $477 top ticket price.

The cheerful, naughty extravaganza by “South Park” masterminds Trey Parker and Matt Stone, with songs by Parker and “Avenue Q” composer Robert Lopez, was lavished with nine Tony Awards (best musical, book, score, etc.) and hosannas from the New York Times as “the best new musical (so far, anyway) of the 21st century.” This spring the show got iffy reviews from British critics but set a single-day London sales record anyway, with its top regular prices (72.50 pounds, or about $110) and premium tickets (125 pounds/$190) the highest in the West End

When “Mormon” tickets went on sale here last winter, the Kennedy Center Web site crashed, swamped by a wave of would-be buyers that was “beyond unprecedented,” a Kennedy Center spokesman said. “Mormon's” six-week Opera House run starts Tuesday, and it’s nearly sold out. Most remaining tickets are going for $200-$250.

So it’s pretty big, this jolly show with foulmouthed singing and absurdly sunny dancing as young Mormon missionaries recruit in bloody Uganda. But why? Simply swaggering onto Broadway with the “South Park” brand can’t explain it.

“I am mystified to a degree that people would like it at all,” Lopez says from Brooklyn. “I didn’t expect anything near this size. I never thought I’d get to replicate the success of ‘Avenue Q.’ ”

“In a way, Bobby is the one with the Midas touch,” Stone, on the phone from Los Angeles, says of the now two-time Tony winner Lopez. “And Trey knows musical theater pretty damn well. We expected ‘South Park’ fans, but we didn’t expect traditional musical theater fans to embrace it so positively.”

They have, wherever this unholy showbiz lampoon hath alighted. Take Cleveland, the tour stop immediately before Washington: in front of the Palace Theatrer on a recent weekday, about a hundred people sign up for a chance to snag a handful of $20 front row seats that “Mormon” sets aside most nights. Names are drawn to cheers and groans as a mere 16 tickets get claimed by the lottery’s winners. When a man named Tim wins, he buys only one ticket, not his allotted two.

“Tim should take me!” a woman says at full volume.

The Palace is part of a 10-stage complex in Cleveland’s Playhouse Square district, which dates back to the turn of the 20th century. It’s a true vaudeville-era palace, built by impresario Edward F. Albee (adoptive grandfather of the famous playwright). Think D.C.’s Warner Theatre, only 1,000 seats bigger: the Palace holds 2,800. When the Palace opened in 1922, it boasted the world’s largest electric sign; its grand marble columns and glowing chandeliers are in first-rate shape.

On a sold-out Wednesday night, it feels as if there are more people in the lobby of the Palace than on the streets of Cleveland.They’re all ages, skewing older, conservatively dressed. Tonight, this slice of Middle America doesn’t bat an eye at the f-bombs, sex gags and doctrinal skepticism.

Word must be out about “South Park.”

“At first I thought: This is really mild for them,” a woman can be heard saying as the satisfied throng pours into the Ohio night. She’s talking about the show’s innocent opening moments, before the blasphemous knockoff of “Hakuna Matata” and the entrance of the rebel warlord with the filthy name.

This is what it’s like everywhere, according to Mark Evans and Christopher John O’Neill. Evans plays Elder Price (the tall, entitled young missionary) and O’Neill is Elder Cunningham (his plump, funny sidekick), and they’ve done the show in a dozen North American cities this year.

The variety of people embracing the musical “shows you how expansive America is,” says Evans, who is originally from Wales.

O’Neill, sitting with Evans in a coffee shop across from the theater before the performance, says “Mormon” draws everyone from teenagers to, as he puts it, “90-year-old subscribers. And they’re the first ones up dancing at the end.”

The mainstream appeal is partly due to how “Mormon” has been marketed, emphasizing the ebullient sweetness that redeems all the comic sin. But as the creators will tell you, there’s also something about how the musical was made.

“There is a misconception out there that Trey and I brought the funny and Bobby wrote the music,” Stone says. “It wasn’t like that. Trey can hold his own with melodies, and Bobby is funny as s---. I’m the lucky guy that gets to sit there and hang out with these two geniuses.”

“We all wrote the songs together,” Lopez attests. “We were all always in the room, making each other laugh.”

Parker briefly attended the famed Berklee College of Music, and songs have been part of the Parker-Stone arsenal since their very early “Cannibal! The Musical.” But set aside the taste-baiting content of “Mormon,” which not so long ago might have been regarded in the same light as “Springtime for Hitler.” The show’s form has all the comfortably familiar ingredients of – well, of a lot of popular American musicals.

For Lopez, the story always boiled down to “The Music Man.” (Like Professor Harold Hill in that show’s troubled River City, Elder Cunningham runs a bit of a con on the Ugandan natives — but, of course, his heart is in the right place.) “Hasa Diga Eebowai” baldly sends up “Hakuna Matata,” but Lopez cites plenty more influences, from “The Telephone Hour” in “Bye Bye Birdie” to Up With People and Disney composer Alan Menken's “I want” anthems — songs in which the hero/heroine sing about his/her dream.

“We always worked from models,” Lopez says.

“Trey and I are totally unabashed about that,” says Stone, noting that they revisit cultural touchstones like “Star Wars” almost weekly.

Lopez adds that with material as dicey as “Mormon” — imagine an over-the-top “South Park” song and dance number set in hell, and you’ll get a feel for the irreverent extremes — “You don’t want to stray too far from the traditional look and feel of Broadway musicals.”

Not that these cutups slapped the show together from spare parts. The musical was almost seven years in the making, and often half a year would go by between writing sessions, since Parker and Stone were on the West Coast and Lopez was in New York. Trying to recall what they’d done, Stone says, “We would have to rehash it again, almost like an oral tradition.”

Their concept eventually went beyond religion and tapped into “class, race — there’s so much material to bounce off of,” Stone says. “You get to go really high-low with the whole thing. You get to talk about colonialism, and you get to talk about poo.”

Casey Nicholaw, choreographer of the Monty Python lark “Spamalot” and director-choreographer of “The Drowsy Chaperone,” was eventually brought in to co-direct with Parker and to add the often hilarious choreography that helps set the show’s tone. “He didn’t hold back at all,” Lopez says. “The show grew over many years, and the last stage was glitzing it up.”

The business angle of all this has something to do with the lore of the tight ticket. “Mormon” is playing in a comparatively small house for a Broadway musical, the 1,100-seat Eugene O’Neill, while “Lion King,” “Wicked” and “Spider-Man: Turn Off the Dark” entertain 1,700, 1,800 and 1,900 a night, respectively, according to The Broadway League. “Mormon” seats are simply harder to come by.

Who knew the show would be in such high demand when they landed the cozy O’Neill? Lopez, in fact, monitored the online ticketing agency nightly during the run-up to opening. Scoring 20 tickets was discouragingly easy.

“I was worried,” Lopez says. (The sellouts began, he recalls, with preview performances and word-of-mouth.)

At the same time, “Mormon” has plainly cultivated a strategy of scarcity. Evans says you’ll find far fewer illicit YouTube peeks of “Mormon” than of “Wicked,” and in this online age little official video has been released. Lopez says that means fans wanting to experience the show again need to head back to the theater.

On tour, Stone acknowledges that they’ve been careful not to overstay the show’s popularity. “We didn’t want to limp out of any city,” he says.

Stone also believes in the effect of full houses on performers. “We want them to keep putting on a good show,” he says, contending that the buzz of a sellout keeps the actors’ energy up. “When the cast does the show well, whatever cast it is, it’s a great show.”

“That’s it,” Stone concludes. “That’s my revelation.”

The Book of Mormon

Book, music and lyrics by Trey Parker, Robert Lopez and Matt Stone. Tuesday through Aug. 18 at the Kennedy Center Opera House. Call 202-467-4600 or visit