NOTATION: $O_x$ -- the product of all odd primes $\le x$.

E.g. $O_7=3\cdot 5\cdot 7 = 105$.

QUESTION: Are the order pairs $(d\ p)=(1\ 3)$ and $(d\ p)=(4\ 5)$ the only solutions of the equation: $$|O_p-2^d|=1$$ in a natural number $d$, and an odd prime $p$?

(I don't know an answer).