In 2005, a maximum security prison staged the greatest play you’ve never seen.

“Breakin’ the Mummy’s Code” was the brainchild of Rehabilitation Through the Arts (RTA), a theater program for incarcerated men at New York’s Sing Sing Correctional Facility. The original musical was written and performed entirely by the group, who played gladiators, mummies, cowboys and pirates in the ingenious time-traveling romp.

“During the course of our day, we didn’t really have a lot of reasons to smile,” says Clarence “Divine Eye” Maclin, who portrayed Hamlet and Robin Hood in the production. “Coming together at those times – and watching everybody let their guard down and be silly – those are the great moments I remember about creating this particular play.”

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The musical’s conception is now the backdrop for “Sing Sing” (in theaters nationwide Friday), a stirring new film starring Colman Domingo as the real-life John “Divine G” Whitfield, who spent nearly 25 years behind bars on a wrongful homicide conviction. The movie traces Whitfield’s decades-long fight for clemency, as well as his involvement in RTA.

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Director/co-writer Greg Kwedar learned about the program through a Google search, stumbling upon a 2005 Esquire article by John H. Richardson titled “The Sing Sing Follies.” He was instantly drawn to the stark contrast between prison life and the insanity of “Mummy’s Code.”

“There was something about the playfulness of the work itself, juxtaposed with the environment it was in, that felt like the full human experience,” Kwedar says. “It was joyous; it was the energy of it.”

'There was a lot of trauma going back into that space'

Save for a few professional actors, including Paul Raci (“The Sound of Metal”), the movie’s cast is comprised almost entirely of formerly incarcerated men. Sean “Dino” Johnson served 15 years at Sing Sing on a drug-related charge and was released in 2004. He was a founding member of RTA, and jumped at the opportunity to flex his acting muscles again.

“I’ve been home now 20 years and I had to pay the bills. I didn’t have time to live my dream and do the acting thing,” Johnson says. “So when Greg offered that opportunity, I was like, ‘You know what? Now’s the perfect time.’ ”

For Maclin, it was similarly “a no-brainer.” He spent 17 years at Sing Sing for robbery and was released in 2012. Since then, he says that RTA has been approached about many film and TV projects, but none of them felt “genuine.”

“Every time we talked to someone, it felt like they were going to use us,” Maclin says. “They just wanted to be able to say they helped some poor prisoners, so they could go home and sleep well at night.” But he didn’t get that feeling with Kwedar and his co-writer, Clint Bentley: “They were sincere about their endeavors and what they wanted to do.”

Both Maclin and Whitfield received a story credit on the film, and helped to ensure that the dialogue was authentic to a prison setting. Kwedar also hired an on-set therapist, in case any of the men felt triggered during production. (The movie was shot at Downstate Correctional Facility, where many cast members passed through on their way to Sing Sing.)

“There was a lot of apprehension,” Maclin says. “Nobody wants to voluntarily go back into a prison that you were held in, much less put on that same prison garb that characterizes you as property of the state. But we understood that the purpose of what were doing outweighed any ill feelings we had.”

For Johnson, “there was a lot of trauma going back into that space: the walls, the smell, the stagnant air. It just brought it all back for me. However, I knew there was a difference: Years ago, I didn’t care how a state green (uniform) fit me. But this time, I was like, ‘You know what? Let me find one that looks good on me.’ (Laughs.) My whole mindset was, ‘This is a choice. This is not mandatory. This is not punishment. The doors are open and I can walk out whenever.’ ”

'This is a lot bigger than a bucket list'

The cast and crew leaned on each other throughout the frequently emotional shoot. (“They got used to seeing me cry,” Kwedar jokes.) That kinship is apparent as they promote the critically acclaimed film, which multiple Oscar pundits have already declared the early frontrunner for best picture. Maclin, too, is widely predicted to earn a best supporting actor nod for his remarkable screen debut.

“As far as nominations and Oscars, I think that Colman Domingo is much more deserving,” Maclin humbly deflects, before Kwedar cuts in with praise for the whole ensemble.

“It’s weird to think about individualized awards for what was such a communal process,” says the filmmaker. “That’s something to reckon with as time goes on – we all want to celebrate each other, and not disregard that immense personal work went into this across the board.”

Both Maclin and Johnson plan to continue acting, and have a long list of Hollywood stars they’d love to work with: Denzel Washington, Halle Berry, Tom Hanks and Sandra Bullock, among them. Their dream project is a remake of “The Dirty Dozen” with other RTA alumni.

Premiering “Sing Sing” at Toronto Film Festival last fall, Maclin was “blown away” to see how audiences connected to their story. It was the first time that an acting career truly felt attainable: “When they stood up, I realized this is a lot bigger than a bucket list.”

Johnson, too, was heartened by the warm embrace. “For so many years, we’ve been trained to think that the world is not interested in the formerly incarcerated,” he says. But ultimately, this is a movie “about people. We all go through things. The human spirit is so strong, and we all have our breaking points.”