Mitra–Paul–Sarkar's conjecture on primes in multiplicative intervals

Let $m,n\in\mathds{N}$, let $\pi(x)$ denote the prime-counting function, and let $\lceil\cdot\rceil$ denote the ceiling function. Mitra–Paul–Sarkar's conjecture. If

$$n\geq \lceil 1.1\log 2.5m\rceil,$$

then

$$\pi(mn)-\pi(n)\geq m-1.$$

This conjecture gives a lower bound for the number of primes in the interval $(n,mn]$. The source presents it as a conjecture of Mitra, Paul, and Sarkar; its resolution status is not established in the supplied text.