Many consider Ada Lovelace to be the first programmer. An article from a couple days ago asks what did her program do?
In a sense, nothing. It was written for a computer that did not exist, so it was never executed. But it was written to compute the 8th Bernoulli number.
The article’s author created a translation of Lovelace’s program into C.
The program to compute the Bernoulli numbers in Note G of the Memoir was not the first computer program. Babbage demonstrated other programs for his Analytical Engine during the conference in Turin of which the original Memoir in French, which Lovelace translated into English, is a description. That French Memoir also contains descriptions of programs for the Analytical Engine.