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Let $p$ be a prime dividing $a$. Clearly, $a$ and $p$ are odd, so $a-p$ is even so that $n-p<2022$, once if $a-p$ were greater than $2022$, $a$ could be written.
সংখ্যা প্রতিস্থাপন
At first, a natural number $a$ is written on the board. Then, at each minute, Muttakin chooses a divisor $b>1$ of $a$, erases the number $a$ from the board, and writes the number $a+b$ there. After that, Muttakin continued to do this again and again. If the first number on the board is $2022$, what will be the largest composite number that Muttakin will never be able to write on the board?
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