Comment by susam
12 hours ago
One of my favourite Grothendieck stories from <https://www.ams.org/notices/200410/fea-grothendieck-part2.pd...>:
> One striking characteristic of Grothendieck's mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called "Grothendieck prime". 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."
I had to follow your link to get it: I hadn't realized that 57 is not prime. At least I'm in good company.
It looks like a prime, but can be caught with the second-simplest test: sum of the digits is 12, which is divisible by 3. Hence it's divisible by 3.
(The simplest test being of course if the number is even and bigger than 2)
Edit: now that I think about it, probably should not have tried to impose ordering to the simplicity of tests. There's of course the divisibility by 5 test, which is even simpler.
John H Conway proved that the smallest number which looks prime, but isn’t is 91. https://youtu.be/S75VTAGKQpk?si=fCGilXECmCOy7T7R
“This is an important theorem, and a result I’m very proud of.”
I just noticed that it's 60-3 without any divisibility tests.
Tao's 27 prime was much more embarassing but understandable as he's no a calculator.
Savants are for things like remembering the first million primes. Someone like Tao or Grothendieck can't remeber them beyond 20, but it doesn't mean they can't actuly reason about them.
In fact, most 2 digit numbers not divisible by 2, 3, or 5 are prime. [1] The only one that's likely to ruin your day is 7 * 13 == 91, but that's self-defeating because after you think about it long enough 91 falls victim to [2].
[1] https://til.andrew-quinn.me/posts/most-2-digit-numbers-not-d...
[2]: https://en.wikipedia.org/wiki/Interesting_number_paradox
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It's referred to as the Grothendieck Prime for this reason.
Take 111 as an example.
27 is a Tao prime. Terence Tao suggested 27 was a prime number on The Colbert Report in 2014. He was likely very nervous.