# What about an alternative formulation for different prime constellations in the spirit of Suzuki's theorem for twin primes?

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).

## 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.

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