Story of Grothendieck's Prime Number

Question

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.

Edit: 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 (strangely) calls a legend...

Cross-posted at Mathoverflow: https://mathoverflow.net/questions/326912/story-of-grothendiecks-prime-number

Answer 1

While it certainly does not confirm (nor refutes) Grothendieck's episode, the fact that Hermann Weyl did commit this mistake might add some 'substance' to it

The notion of prime number is of course as old and as primitive as that of the multiplication of natural numbers. Hence it is most surprising to find the distribution of primes among all natural numbers is of such a highly irregular and almost mysterious character. While on the whole the prime numbers thin out the further one gets in the sequence of numbers, wide gaps are always followed again by clusters. An old conjecture of Goldbach's maintains that there even come along again and again pairs of primes of the smallest possible difference 2, like 57 and 59.

in Weyl, H. (1951). A half-century of mathematics. The American mathematical monthly, 58(8), 523-553.

Answer 2

Theoretical mathematicians and physicists often make calculational errors. And it seems that this is the case here. The numbers that theoretical mathematicians often use are one or two with the rest having a vanishing small probability of occuring. Hence, it's not surprising they make mistakes.

Without actually being comfortable with using prime numbers on a daily basis, I would have said 57 was prime. Like Grothendieck did. Though of course, I'm not comparimg myself to him in any way. Another example is a theoretical physicist who is interested space and geometry but who often mixes up his left and right - like I do - and have just done so in the last hour or so.