[stracer]

The third source is still wrong, as Planck certainly would not agree that he used the photon argument to make a prediction. He tried to explain the experimental data on blackbody radiation, which manifested the spectral peak, and an agreement with the Rayleigh-Jeans and Wien laws in the two frequency limits. Thus not a prediction, but an explanation of the observed thing.

And he did not believe in photons, he interpreted his work in terms of classical EM radiation obeying some entropy condition, and quanta of energy that he used were considered either a math trick to make calculations with that entropy, or a condition on the emission process only in his later theories. He never assumed or believed that EM radiation consists of quanta.