Number Theory

    

Conjecture on the Quadruplets of Primes of the Form (P, P+4k^2, P+6k^2, P+8k^2)

Authors: Marius Coman

In a strict sense, the term “prime quadruplet” refers strictly to the primes (p, p + 2, p + 6, p + 8) - see Wolfram MathWorld; it is not known if there are infinitely many such prime quadruplets. In this paper I conjecture that for any k non-null positive integer there exist an infinity of quadruplets of primes of the form (p, p+2k^2, p+6k^2, p+8k^2). Finally, I define the generalized Brun’s constant for prime quadruplets of the type showed and I estimate its value for the particular case k = 2 (for k = 1 the value it is known being approximately equal to 0.87).

Comments: 3 Pages.

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[v1] 2015-12-18 09:51:28

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