I asked this question earlier, at hsm.stackexchange.com without much luck. Maybe somebody can answer it here.

There is a story about Alexander Grothendieck and the "Grothendieck Prime" 57, which goes roughly as follows (cf. this wikipedia article):

In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”

This quote is taken from Allyn Jackson's article "Comme Appelé du Néant— As If Summoned from the Void: The Life of Alexandre Grothendieck". Jackson refers to the story as a "legend". One can argue that the story is quite believable given Grothendieck's way of thinking (David Mumford: "He (Grothendieck) doesn’t think concretely").

Question. What (if any) is the factual basis of the story?

For instance, when/where did it happen? (In different versions it is said to have happened during or after a Grothendieck's talk.) Did anybody hear this story from somebody present at Grothendieck's talk?

My guess is that the story is just a legend, but I could be mistaken.

Just for the sake of completeness, here is what Georges Elencwajg had to say about this issue (extracted from my conversation with him in comments to an answer to this math.stackexchange question):

The story is not made up: Grothendieck did make that silly blunder, in an exchange after a talk, after being asked to be more concrete by a member of the audience. Of course this doesn't change anything to the fact that Grothendieck was one of the most profound arithmeticians of the 20th century. And indeed 57 looks a bit prime for some psychological reason :-) . Conversely many mathematicians think I'm pulling their leg when I tell them that 4999 is prime! ... I've heard this story a long time ago. I think it is true but I can't prove it since, alas, most of the protagonists are dead. Anyway, this is just an amusing but quite meaningless anecdote: a genius made a lapsus linguae. So what? On the other hand I'm quite sure that Allyn Jackson can't disprove what he [sic] (strangely) calls a legend...

In contrast, here is what Franz Lemmermeyer said at HSM:

There is a similarly inane story about Kummer not being able to work out 7⋅9, or about Gauss on the number of needles on a Christmas tree. I have no idea why people continue to disseminate such stories without giving a reference - this is a very idiotic behavior even if you call the story a legend.

Update. According to an answer on HSM, Herman Weyl in

A half-century of mathematics. The American Mathematical Monthly, vol. 58 (1951) p. 523-553.

explicitly stated that 57 is a prime number. Accordingly, my current conjecture is that the actual origin of Ally Jackson's story is that somebody misremembered and attributed to Grothendieck a mistake made by Weyl.

I asked this question earlier, at hsm.stackexchange.com without much luck. Maybe somebody can answer it here.

There is a story about Alexander Grothendieck and the "Grothendieck Prime" 57, which goes roughly as follows (cf. this wikipedia article):

In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”

This quote is taken from Allyn Jackson's article "Comme Appelé du Néant— As If Summoned from the Void: The Life of Alexandre Grothendieck". Jackson refers to the story as a "legend". One can argue that the story is quite believable given Grothendieck's way of thinking (David Mumford: "He (Grothendieck) doesn’t think concretely").

Question. What (if any) is the factual basis of the story?

For instance, when/where did it happen? (In different versions it is said to have happened during or after a Grothendieck's talk.) Did anybody hear this story from somebody present at Grothendieck's talk?

My guess is that the story is just a legend, but I could be mistaken.

Just for the sake of completeness, here is what Georges Elencwajg had to say about this issue (extracted from my conversation with him in comments to an answer to this math.stackexchange question):

The story is not made up: Grothendieck did make that silly blunder, in an exchange after a talk, after being asked to be more concrete by a member of the audience. Of course this doesn't change anything to the fact that Grothendieck was one of the most profound arithmeticians of the 20th century. And indeed 57 looks a bit prime for some psychological reason :-) . Conversely many mathematicians think I'm pulling their leg when I tell them that 4999 is prime! ... I've heard this story a long time ago. I think it is true but I can't prove it since, alas, most of the protagonists are dead. Anyway, this is just an amusing but quite meaningless anecdote: a genius made a lapsus linguae. So what? On the other hand I'm quite sure that Allyn Jackson can't disprove what he [sic] (strangely) calls a legend...

In contrast, here is what Franz Lemmermeyer said at HSM:

There is a similarly inane story about Kummer not being able to work out 7⋅9, or about Gauss on the number of needles on a Christmas tree. I have no idea why people continue to disseminate such stories without giving a reference - this is a very idiotic behavior even if you call the story a legend.

Update. According to an answer on HSM, Herman Weyl in

A half-century of mathematics. The American Mathematical Monthly, vol. 58 (1951) p. 523-553.

explicitly stated that 57 is a prime number. Accordingly, my current conjecture is that the actual origin of Allyn Jackson's story is that once upon a time, somebody misremembered and attributed to Grothendieck a mistake made by Weyl.