Let p_1 < p_2 < p_3 < \ldots < p_n < \ldots be the sequence of primes (with p_1 := 2 as usual).
Conjecture: There are infinitely many positive integers n for which
\begin{eqnarray} p_n + p_{n + 3} - 2 p_{n + 2} = 0. \end{eqnarray}
For example, the above relation holds for n = 2 since p_2+ p_5 - 2p_4 = 3 + 7 - 2 \times 5 = 0. Follow technical thread here.
No comments:
Post a Comment