On the Twin-Prime Problem I

Turán, P. (1964) On the Twin-Prime Problem I. A MAGYAR TUDOMÁNYOS AKADÉMIA MATEMATIKAI KUTATÓ INTÉZETÉNEK KÖZLEMÉNYEI, 9 (3). pp. 247-251.

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Abstract

The twin-prime problem, which was stated by LANDAU in his Cambridge-Congress lecture in 1912 as the second main problem of the analytical number theory asks whether or not there exists an infinity of prime-pairs (p, q) with p - q = 2 or more generally with p - q = 2l (l fixed integer). This problem is unsolved up to now though the first explicit remarks on it were made probably by Euler. The classical paper of Hardy and Littlewood¹ laid down the fundaments of an analytical treatment of additive number theoretical problems and made clear the deep connection of them with the distribution of zeros of Dirichlet's L-functions.

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