Some Twin Primes

With n_{32} representing the sum of all primes smaller than 2^{32}, the number n_{32}-1 = 425649736193687429 is a member of the twin prime \left(425649736193687429, 425649736193687431\right). The numbers n_{7} + 1 and n_{34} + 1 are also twin primes: \left( 1721, 1723 \right) and \left( 6400753258957522037, 6400753258957522039 \right) respectively.

It is unknown if that information is of any use but as the saying goes: “You’ll never know!”.


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