  We study the distribution of the values of the form $\lambda_1 p_1 +
\lambda_2 p_2 + \lambda_3 p_3^k$, where $\lambda_1$, $\lambda_2$ and
$\lambda_3$ are non-zero real number not all of the same sign, with $\lambda_1
/ \lambda_2$ irrational, and $p_1$, $p_2$ and $p_3$ are prime numbers. We prove
that, when $1 < k < 4 / 3$, these value approximate rather closely any
prescribed real number.
