Infinite primes history

Question

I am little confused with who was the first to modify Euclid's argument of infinitude of primes from $p_{1}p_{2}...p_{r}+1$ to $p_{1}p_{2}...p_{r}-1$? Some writers say it was E.E. Kummer ,($1878$) (Ref: Ribenoim's book 'the new book of prime records') .Some say it was J. Perrot (Ref: Euclid's theorem on the infinitude of primes , Romeo mestrovic, page:$9$, $2$nd last line). Which one is correct? Any help with the reference will be appreciated. I am adding a picture of Ribenoim's book.

Also I am unable to find the following paper (translation into English , Collected Papers, II, 669–670, Springer, Berlin-Heidelberg, 1975) E. E. Kummer, Neuer elementarer Beweis des Satzes, dass die Anzahl aller Primzahlen eine unendliche ist, Monatsber. Preuss. Akad. Wiss., Berlin 1878/9, 777–778. [Collected Papers, II, 669–670, Springer, Berlin-Heidelberg, 1975.]

Thanks in advance.

Added

Answer 1

Kummer wouldn't have bothered to republish Euclid's proof with a $-$ instead of $+$, in particular since the proof does not work if you start with $p_1 = 2$. Kummer's proof uses Euler's phi function; see https://www.biodiversitylibrary.org/item/111278#page/880/mode/1up As a rule, Ribenboim's attributions are to be taken with a large grain of salt. Most of his references in FLT for amateurs aren't worth anything since he didn't check the originals.

P.S. If you're looking for old manuscripts on the web, search for the journal, not the title.

Answer 2

According to Euclid's theorem on the infinitude of primes: a historical survey it was Perott, who first remarked that $p_1\cdots p_r-1$ also works, see page $9$. The linked paper gives a wealth of historical references.