Earlier quoted context omitted.
It was the first published program but not the first. To be the first, you have to believe Babbage designed a general purpose computer that could accept instructions and never wrote any instructions. https://www.bbvaopenmind.com/en/ada-lovelace-original-and-vi... “I confirm that the manuscript evidence clearly shows that Babbage wrote ‘programs’ for his Analytical Engine in 1836-7 i.e. 6-7 years before the publicatio…
It really depends what you mean by "program". Would you argue that the Euclidean algorithm from two millenia prior was a program? Ada Lovelace was the first to realise that the analytical engine would perform arbitrary tasks and wrote programs for those arbitrary task, beyond computational operations. Of course Babbage who designed the hardware had some idea of what programs it could run and presented examples, but h…
A [computer] program is a sequence of instructions executable by a machine (the computer).
> Would you argue that the Euclidean algorithm from two millenia prior was a program?
It's in the name: EA is an algorithm.