Interesting quintuple of primes.

[David W. Wilson]

Let S = {13, 5197, 5701, 6733, 8389}. Then

 

                S has 5 elements.

                Every element of S is prime.

                The concatenation of any two distinct elements of S is
prime.

 

The sum of S is 26033. No other set with sum <= 26033 has these properties.

 

I don't know if I am the first discoverer.

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