A plane $\mathrm{\pi }$ passes through the point $(1,1,1)$. If $b,c,a$ are direction ratios of a normal to the plane $\mathrm{\pi }$, where $a, b, c (a < b < c)$ are the prime factors of 2001, then the equation of plane $\mathrm{\pi }$ is

The prime factors of $2001$ are $3,23,29$

Here $a=3,b=23,c=29$

Direction ratios of the normal to the plane is 

since the plane is passing through the point $\left(1,1,1\right)$, $23x+29y+3z=d$ must satisfy the point $\left(1,1,1\right)$

Hence, the equation of the plane is $\boxed{23x+29y+3z=55}$