1723

This number is a prime.

English broadcaster, author and parliamentarian Melvyn Bragg discussed prime numbers (like 1723 for example) during the BBC Radio 4 documentary series "In Our Time" on 12 Jan 2006.

Proving the Riemann Hypothesis is equivalent to showing floor(H(n)+e^{H(n))*log(H(n)}) ≥ σ(n), where H(n) = 1 + 1/2 + 1/3 + ... + 1/n, and σ(n) is the sum of the divisors of n. For example, when n = 17, the two sides differ by 23. [Caldwell]

The prime that splits into the two primes, 17 and 23, which are the extremal constants of the magic triangle of Yates using digits 1 through 9:

       1                 7 

     9   6             3   6 

   5       7         5       1 

 2   8   4   3     8   2   4   9

The smallest distinct-digit emirp concatenated from two double-digit primes. [Loungrides]