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I was talking with a student of mine about Goldbach's conjecture, and a certain point he asked why this apparently simple statement is so difficult to prove.

Half-joking, I answered "well, because prime numbers are made to be multiplied, not added", explaining that it is a well-known quote by Lev Landau, or at least this is what a Google research shows (see for instance here).

However, I was unable to find any authoritative source supporting this attribution. This led me to ask what follows:

Q. Is this quote really by Landau? If so, what is the original source? Is it written in some of his papers, or is there some historical account supporting this credit?

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    $\begingroup$ Probably exactly the same Google research you did turns this up in an opinion piece by Arnol'd: p. 8, "'Why add prime numbers?' marvelled the great physicist Lev Landau. 'Prime numbers are made to be multiplied, not added!'" Of course this doesn't answer the question, but maybe suggests an answer like "he said it to Arnol'd"? $\endgroup$
    – LSpice
    Commented Dec 16, 2017 at 22:59
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    $\begingroup$ Maybe, just maybe, it would be better to ask that here: hsm.stackexchange.com $\endgroup$
    – user114642
    Commented Dec 16, 2017 at 23:00
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    $\begingroup$ Well, Arnold's statement seems not very far away from the answer I gave to my student: did Landau really said this to Arnold, or Arnold just used the sentence as a "well-known" Landau quote? Secondly, I agree that asking on the forum of history of science could be an option, however there is still a tag "history" on MO. And it is still used, as far as I can see. $\endgroup$
    – Francesco Polizzi
    Commented Dec 16, 2017 at 23:07
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    $\begingroup$ Landau said this not to Arnol'd but to Vinogradov, or at least on the occasion of Vinogradov's work on the Goldbach conjecture, in the 1930s, when Arnold was not old enough to have a conversation on the subject. $\endgroup$
    – Igor Rivin
    Commented Dec 17, 2017 at 0:17
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    $\begingroup$ @IgorRivin I believe it was Abraham Lincoln who said that quotes on the web are often misattributed $\endgroup$
    – Will Jagy
    Commented Dec 17, 2017 at 1:00

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