When he was 24 years old, Paul McCartney famously looked a few decades into the future to record “When I’m Sixty-Four,” the Beatles tune about growing infirm by the fireside.

Back then, the song functioned as a cozy prediction. Yet once McCartney reached that age in real life — and was still out flipping his perfect hair all over the place — “When I’m Sixty-Four” became something of a comical object lesson: proof that even a beloved Beatle underestimated how long a formative rock ‘n’ roller might stick around.

McCartney is 76 now, and earlier this month he released a new studio album, “Egypt Station,” just days before he launched his latest tour in Quebec City.

McCartney isn’t the only 76-year-old songwriter called Paul with a record this month.

Paul Simon, who in his mid-20s pictured a future on a dusty park bench in Simon and Garfunkel’s “Old Friends,” also has a new album, “In the Blue Light.” Like Mc- Cartney he’s preparing to hit the road, in his case before he retires from touring.

But McCartney and Simon have shared more than an age and a first name on their respective journeys toward lucrative hero status.

Both were inducted twice into the Rock & Roll Hall of Fame, first as members of a group and then as solo acts. Both were nominated for at least one Grammy Award for album of the year in every decade between the 1960s and the 2000s.

More dubiously, in the early ’80s both wrote and starred in quasi-biographical movies — McCartney’s “Give My Regards to Broad Street” and Simon’s “One-Trick Pony” — that make it clear nobody has ever been eager to tell these two “no.”

Yet what’s remarkable about “Egypt Station” and “In the Blue Light,” especially considering their release on the same day — Sept. 7 — is how differently each man is going about the business of late-stage pop stardom — differently from each other, that is, and from their peers.

Neither of these projects is an affectionate excursion into the Great American Songbook like those we’ve seen from Rod Stewart and Bob Dylan (and indeed from Mc- Cartney, who tried his hand at Frank Loesser and Irving Berlin on “Kisses on the Bottom” in 2012). And neither is a back-to-basics effort a la the Rolling Stones’ recent “Blue & Lonesome” or one of Rick Rubin’s stripped-down productions for Johnny Cash or Neil Diamond.

Instead, McCartney and Simon each seem intent in their own way on pushing ahead, even when that means taking up the past.

The built-in takeaway from “Egypt Station” is that McCartney recorded the bulk of the album with Greg Kurstin, the hit-making producer known for his work with the likes of Pink and Kelly Clarkson.

Long and winding road

It’s not the first time the former Beatle has recruited an au courant collaborator; his previous album, 2013’s “New,” featured tracks variously produced by a number of them, including Mark Ronson and one of Adele’s right-hand men, Paul Epworth.

But the scattershot approach on “New” suggested a kind of strategic gambit, whereas “Egypt Station” has a more creative, unified feel. (Depending on your taste, you’ll be either relieved or disappointed to discover that it’s not a radio-ready turbo-pop disc.)

The idea it puts across is that McCartney wanted to test his singingand songwriting against the conventions of modern record-making — to find out whether he’s kept his skills sharp enough to shine outside a strict legend-at-work context.

The answer, often enough, is yes.

More rigorously quality-controlled than any album McCartney’s released in years, “Egypt Station” is consistent with its pleasures: the tuneful guitar crunch, the swelling piano parts, the crisp vocal harmonies that float just so over grooves that somehow bounce and thud at the same time.

Inevitably, there are highlights, such as the sweetly strummy “Happy With You” (in which he contrasts his current life with what sounds like the dark days after the Beatles’ breakup) and “Back to Brazil,” a delightful little electro-pop ditty that reminds you how many modern record-makers (from Kurstin to Ariel Rechtshaid) probably had their minds blown by McCartney’s early solo stuff.

There are lowlights too: “Caesar Rock,” for instance, is hardly even a song; it’s basically just a riff and a beat — either of which would’ve been better used in one of a handful of shape-shifting tunes (including “Despite Repeated Warnings” and “Hunt You Down/Naked/C-Link”) that nod toward the zany structures McCartney deployed during his days with Wings.

With its grabby textures and insinuating melodies, though, “Egypt Station” sounds like it was tailored to the streaming era.

What’s he singing about? Memories, companionship and, like any pop star, an endlessly renewable appetite for sex.

In the jaunty “Come on to Me” he’s a guy who’s met a woman at some social function. “We need to find a place where we can be alone,” he tells her, “To spend some special time without an interruption.”

As its title suggests, “Fuh You” — produced in a fist-pumping midtempo style by Ryan Tedder of OneRepublic — is more direct in its proposition.

Part of the implicit draw of these songs is hearing McCartney indulge his raunchy side at 76; here, in contrast with the rest of the album, he’s relying almost entirely on his extra- musical star power.

But who wouldn’t pull that out if he had it? As James Corden’s recent “Carpool Karaoke” segment with McCartney demonstrated for merely the latest time, we’re talking about someone in whose presence fans are compelled to confess their devotion so earnestly that it hurts.

McCartney couldn’t escape that legacy if he tried (which he never will). But he wears it lightly on “Egypt Station” — as much a moral achievement as a musical one.

Rethinking his old songs

Simon’s history weighs more heavily on “In the Blue Light,” which is understandable given that he performed his final shows in New York last weekend as part of what he’s calling his farewell tour.

As thousands saw in May at the Hollywood Bowl — where he explained his goodbye to the road doesn’t mean he’s giving up writing new music or performing here and there — Simon’s mode in these concerts is willfully retrospective: He’s putting “a casing” around his half-century in pop, he said onstage, and “look(ing) at it that way.”

But if the material was familiar at the Bowl, many of the interpretations were not; this was an opportunity for Simon to rethink his old songs, in some cases pretty dramatically, rather than to fix them (or fix them further) in the public consciousness.

And it’s that renovator’s eye that he maintains on “In the Blue Light,” which contains newly recorded versions of 10 lesser-known selections from his catalog, beginning with “One Man’s Ceiling Is Another Man’s Floor” (from 1973’s “There Goes Rhymin’ Simon”) and ending with “Questions for the Angels” (from 2011’s “So Beautiful or So What”).

As with McCartney drafting a hot young producer, the concept here isn’t unprecedented; Simon’s onetime touring partner Sting, for one, released a set of orchestral renditions of his hits in 2010.

Yet Simon’s focus on deep cuts — not to mention several arrangements that leave the new takes more jagged than the relatively slick originals — make it hard to view “In the Blue Light” as the self-congratulating cash grab you might expect.

What the album offers instead is an interesting glimpse at the elements this notoriously painstaking creator thinks he got wrong the first time around, such as the elaborate percussion of “Darling Lorraine,” which he presents here in much more spacious form. (“You don’t want to get too busy admiring the drums,” he recently told England’s Telegraph newspaper.)

And it shows his concern for setting a song precisely in its day. On “Rhythm of the Saints,” Simon sings in the Brazilian-accented “Can’t Run But” about a blues band down by the riverbank; now, over choppy strings arranged by Bryce Dessner of the National, he hears a DJ pumping out “sub-bass … like an earthquake.”

Dessner is one of many guest musicians on “In the Blue Light,” along with the guitarist Bill Frisell, who draws out the wide-open twang of “Love,” and Wynton Marsalis, who helps transform “How the Heart Approaches What It Yearns” from plush soft pop into smoldering vocal jazz.

But even when a track threatens to get crowded, Simon reserves plenty of space for his singing, which has lost some flexibility but can still express the complicated emotions he writes about.

For some veteran pop stars, the price of longevity is the work required to disguise one’s age. The lack of shame in Simon’s 76-year-old voice happily disrupts that transaction.