Comment by klelatti
Your argument is that because the 4004 was built to power a calculator that disqualifies it as a microprocessor? Independent of the actual nature of the 4004 itself and its potential applications beyond its first intended use? Can’t see how that makes sense at all.
Your statement about Intel 'pushing back' the date to 1971 also makes little sense given Intel advertised [1] the 4004 as a CPU in Electronic News in Nov 1971.
[1] https://en.wikipedia.org/wiki/Intel_4004#/media/File:Intel_4...
Because of its purpose, Intel 4004 did not have many features that had been recognized as necessary already since the first automatic computers, for example the lack of logic operations, which was mentioned in the parent article.
Therefore I do not believe that it is possible to consider Intel 4004 as a general-purpose processor. It had only the features strictly necessary for the implementation of the Busicom calculator.
The idea to sell 4004 for other uses has appeared long after the design was finished, when Busicom did not want to pay for the chipset as much as Intel desired, so Intel decided to try to sell the chipset to other customers too, and then they thought to advertise it as a "CPU".
Moreover, it is debatable whether Intel 4004 can be considered as a monolithic processor, because 4004 was not really usable without the rest of the chipset, which provided some of the functions that are normally considered to belong into a processor.
The Intel 4004 4-bit "CPU" implemented less functions than the 4-bit TTL ALU 74181, which was general-purpose and which was the main alternative at that time for implementing a CPU, but it had the advantage of including many registers, because the MOS registers were much cheaper in die area than the TTL registers, and these included registers were the reason why a CPU implemented with the Intel 4004 chipset had a lower integrated circuit count than the equivalent implementation with MSI TTL ICs.
Intel's advertisement of 4004 being a CPU was just an advertisement of the same kind of Tesla having a "Full Self-Driving".