Partial summation $\sum_{p\leq X}a_p$ via $\sum_{n\leq X}a_n\Lambda(n)$.

Question

Let $\Lambda$ denote the Von-Mangoldt function and $\{a_n\}_{n\in \mathbb{N}}$ a a sequence of real numbers. Assume that:

$$\sum_{n\le X}a_n\Lambda(n)=O(X^\alpha)\quad\text{for some}\quad \alpha\in\mathbb{R}$$

How we might use the partial summation to get an estimation of the sum $$\sum_{p\le X,\;\;\text{prime}}a_p$$