New Game

Students often find themselves studying only during exam periods, enjoying life in between. In this spirit, the students of the Faculty of Cybernetics have decided to take a break from computer games and have created a new board game called "Number Lotto." This game involves a set of tickets, each represented by a sheet of paper listing consecutive natural numbers within a specified integer interval $[L,R]$. For instance, a ticket with L=2 and R=10 would display the numbers 2, 3, 4, 5, 6, 7, 8, 9, 10.

The game unfolds over several rounds. In the first round, the host always announces the number $2$. In each subsequent round, the host calls out a number that is one greater than the previous round's number. After the host announces a number $i$ in a round, players must cross out all numbers on their ticket that are divisible by $i$ without a remainder. Importantly, players only cross out numbers that have not been previously crossed out. The game continues as long as there is at least one uncrossed number remaining on the ticket.

Consider a ticket with L=2 and R=10. Initially, the ticket displays the numbers 2, 3, 4, 5, 6, 7, 8, 9, 10. In the first round, the host calls out the number $2$, prompting the player to cross out 2, 4, 6, 8, and $10$, leaving $3,5,7$, and $9$ uncrossed. In the second round, the host calls out $3$, and the player crosses out $3$ and $9$, leaving $5$ and $7$. In the third round, the host calls out $4$, but the player crosses out nothing. In the fourth round, the host calls out $5$, and the player crosses out $5$. In the fifth round, the host calls out $6$, and again, the player crosses out nothing. Finally, in the sixth round, the host calls out $7$, and the player crosses out the last remaining number, $7$. Thus, the game for this ticket concludes after $6$ rounds.


Your task is to determine the maximum number of rounds that the given ticket can be played.