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In this paper we introduce a new diophantine equation with prime numbers. Let$[\, \cdot\,]$ be the floor function. We prove that when $1<c<\frac{23}{21}$and $\theta>1$ is a fixed, then every sufficiently large positive integer $N$can be represented in the form \begin{equation*} N=\big[p^c_1\tan^\theta(\logp_1)\big]+ \big[p^c_2\tan^\theta(\log p_2)\big]+ \big[p^c_3\tan^\theta(\logp_3)\big]\,, \end{equation*} where $p_1,\, p_2,\, p_3$ are prime numbers. Wealso establish an asymptotic formula for the number of such representations.

On an tangent equation by primes