1

What is the largest three-digit prime each of whose digits is a prime? - I believe it is 773, but correct me if I'm wrong.

A.Rin
  • 31
  • 5
    The largest 3-digit number whose digits are all primes is $777$ which is not a prime. The next smaller one is $775$ which again is not a prime. The next smaller one is $773$. – dxiv Aug 11 '18 at 02:27

1 Answers1

2

Well, it can't be $9xx$ because $9$ is not prime. Similarly, it can't be $8xx$. Thus you're left with $7xx$ or down.

$7$ is prime, and in reverse order, the first three primes of $7xx$ are $797, 787, 773$. The first two don't pass as they contain $8$ and $9$. Thus $773$ should be the largest such prime.

blub
  • 4,794