Margaret Hamilton is an inspiration, but is she actually still working at age 83? I can't find anything that would indicate she is. For something like the "longest-working programmer" I'd expect them to have been actually "work"-working during that time.
And I think I'd classify Knuth as the slightly different "longest working computer scientist". He's known for his quote "Beware of bugs in the above code; I have only proved it correct, not tried it."
Or perhaps I'd classify him as the somewhat more sycophantic "longest working genius" or "longest working cool guy". Heck, Knuth was uniquely awarded a master's degree for his bachelor's because his work was considered so outstanding, he's an organist and composer, and he's hilarious. I love this quote about him: "If you had an optimization function that was in some way a combination of warmth and depth, Don would be it."
It was my primary role. I coded for many hours every day as CEO. It did make for a lot of long days. I can identify as both CEO and programmer. And musician and other things. No need for gatekeeping.
“The Universal Systems Language (USL) is based on a preventive, development-before-the-fact philosophy that does not allow errors in, in the first place.”
Don't forget Ivan Sutherland and Niklaus Wirth. Fred Brooks joined IBM in 1956 and he's still active in research as well; Cynthia Solomon, there's quite a few
Depending how and whether you count academia, Donald Knuth may have a slightly longer career: https://en.wikipedia.org/wiki/Donald_Knuth
Feels like a decent chance you're third, then. Certainly you're one of the longest-working programmers. Best of luck. :)