MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
show/hide this revision's text 5 deleted 1 characters in body; deleted 11 characters in body

@Álvaro:

  1. Agreed that a proof of the coprimality of any pair of distinct Fermat numbers appears in the very first paragraph of the aforementioned missive from Goldbach to Euler. That is not under discussion here. Thing is that, as Professor Lemmermeyer noted above, Goldbach himself did not seem to notice that this result would (immediately) provide him with a proof of the infinitude of the primes. As I commented before, one of my initials beliefs on this matter was that the exclamation "at quantulum hoc est ad demonstrandum omnes illos numeros esse absolute primos?" in the July 20th letter was somehow implying that Golbach had actually found the connection between both facts. Yet, your knowledgeable comments have just made me changed change my mind on this wrong impression that I initially had.Finally, you

  2. You are absolutely right when you express that the proof given by Hardy and Wright passes through the argument given by Goldbach in his letter to Euler. That's the reason that I said it is kind of weird to see H & W adscribing altogether the result to Pólya.
show/hide this revision's text 4 added 106 characters in body; deleted 4 characters in body; added 23 characters in body

@Álvaro:

Agreed that a proof of the coprimality of any pair of distinct Fermat numbers appears in the very first paragraph of the aforementioned missive from Goldbach to Euler. That is not under discussion here. Thing is that, as Professor Lemmermeyer noted above, Goldbach himself did not seem to notice that this result would (immediately) provide him with a proof of the infinitude of the primes. As I commented before, one of my initials beliefs on this matter was that the exclamation "at quantulum hoc est ad demonstrandum omnes illos numeros esse absolute primos?" in the July 20th letter was somehow implying that Golbach had actually found the connection between both facts. Yet, your knowledgeable comments have just made me changed my mind on this wrong impression that I initially had. Finally, you are absolutely right when you express that the proof given by Hardy and Wright passes through the argument given by Goldbach in his letter to Euler. That's the reason that I said it is kind of weird to see H & W adscribing altogether the result to Pólya.
show/hide this revision's text 3 added 4 characters in body

@Álvaro:

Granted

Agreed that a proof of the coprimality of any pair of distinct Fermat numbers appears in the very first paragraph of the aforementioned missive from Goldbach to Euler. That is not under discussion here. Thing is that, as Professor Lemmermeyer noted above, Goldbach himself did not seem to notice that this result would (immediately) provide him with a proof of the infinitude of the primes. As I commented before, one of my initials beliefs on this matter was that the exclamation "at quantulum hoc est ad demonstrandum omnes illos numeros esse absolute primos?" in the July 20th letter was somehow implying that Golbach had actually found the connection between both facts. Finally, you are right when you express that the proof given by Hardy and Wright passes through the argument given by Goldbach in his letter to Euler. That's the reason that I said it is kind of weird to see H & W adscribing altogether the result to Pólya.
show/hide this revision's text 2 deleted 5 characters in body; edited body
show/hide this revision's text 1