Prime Curios!: 1723

1723
(another Prime Pages' Curiosity)

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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

[Beedassy]

The smallest emirp with distinct digits concatenated from two double digit primes. Note that the sum of its digits is the smallest emirp. [Loungrides]

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