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Comment by cbolton | Hacker News Reader

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.”

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

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.

What's Tao's 27 prime again?

Was mentioned in a twin thread:

"27 is a Tao prime. Terence Tao suggested 27 was a prime number on The Colbert Report in 2014. He was likely very nervous."

there was some interview where he illustrated the idea of a twin prime pair using 27 and 29

It's referred to as the Grothendieck Prime for this reason.

Take 111 as an example.

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