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It is known that the twin prime conjecture is a special case of the $k$-tuple conjecture. See if you want the article with title k-Tuple Conjecture from the encyclopedia Wolfram MathWorld.

On the other hand I know* the Theorem 2 of [1], due to Suzuki, concerning a formulation of the twin prime problem.

Question. Is it possible/feasible to get an alternative formulation, in the spirit of Suzuki's Theorem 2, for different prime constellations/k-tuples? Many thanks.

If the statement is in the literature refer the bibliography, and I try to read it from the literature.

References:

[1] Maria Suzuki, Alternative Formulations of the Twin Prime Problem, The American Mathematical Monthly, Vol. 107, No. 1 (January, 2000).

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This question has an open bounty worth +50 reputation from user142929 ending in 2 days.

Looking for an answer drawing from credible and/or official sources.

  • $\begingroup$ *Few months ago I've read it as a free article view from My JSTOR account $\endgroup$ – user142929 Sep 4 at 21:18
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    $\begingroup$ stating suzuki's result briefly would improve this question $\endgroup$ – kodlu Sep 4 at 21:42
  • $\begingroup$ Many thanks for all comments. $\endgroup$ – user142929 Sep 5 at 5:06

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