When I first heard about “Gutenberg! The Musical!” it sounded like a lot of goofy fun.

The show, written by Scott Brown and Anthony King, stars Josh Gad and Andrew Rannells — the duo from the original cast of “Book Of Mormon” who made that show so enjoyable. This time, they play Bud and Doug, two guys who work in a nursing home but dream of creating a Broadway show they can star in. To attract investors, they’ve rented a big theater for one night so then can put on a backer’s audition, in which they present their latest work, a musical biography of Johannes Gutenberg, the 15th-century craftsman who invented the printing press.

Bud and Doug admit they didn’t know much about Gutenberg, so they Googled him, and found out there isn’t much confirmed information about him. So, they decide their show will be a historical fiction, allowing the duo to make up anything and anyone they desire. Though the story includes quite a few characters, Bud and Doug can’t afford to hire any other actors. So, they take on all the parts in the show, using dozens of yellow trucker hats with names on the front to clue us in to which citizens of the German town of Schlimmer they’re playing, including: Beef Fat Trimmer; a couple of drunks; an antisemitic flower girl; a dead baby; and Gutenberg’s love interest/employee, Helvetica.

The guys are backed up by The Middlesex Six, a band that usually plays weddings and bar mitzvahs — but because of the small budget, Bud and Doug can only hire three of them. The musicians get drawn into the shenanigans a couple of times, but not enough to divert our attention from Gad and Rannells, who are simply hysterical. Their comic chemistry and timing remain perfect, and it’s okay when they mug their way through a few numbers because, after all, they’re not portraying skilled theatre professionals.

“Gutenberg! The Musical!” runs a little over two hours with an intermission, but frankly, towards the end, the concept begins to wear thin and there’s nothing fresh introduced. The whole thing could have been a tight ninety-minute show, even though that seems to be against the rules for Broadway musicals. Considering this is more a loving parody of the form, that rule should have been broken.

Nonetheless, “Gutenberg! The Musical!” is precisely what I expected it to be: goofy and fun. While I thought it had been written recently, the show actually debuted in a shorter version in 2005 at the Upright Citizens Brigade Theatre in New York, then became a full-blown production in London the next year starring its two creators, Brown and King. Then it moved Off-Broadway and won a bunch of awards, and has appeared in regional theaters around the US since. But this is its debut on a big Broadway stage.

The show is playing to sold-out houses at the James Earl Jones theatre, where the evening opens with a voice announcing itself as Deepfake James Earl Jones intoning, “You may remember me from I am your father.” As it goes on to remind attendees to turn off their cell phones and other noisy electronic devices, there’s a quick reference to Mufasa from “The Lion King” before the announcement ends with, “This is CNN.”

It’s a very clever way to set the tone for the silliness that follows.