In the decrem problem of October cook-off. If R>=2*L we can take the smallest prime number greater than R then I think it satisfies the condition. Please help

Suppose L is 2 and R is 5. Clearly R>=2*L.
Next prime greater then R is 7.
7%2 is 1, 7%3 is 1, 7%4 is 3,

So this logic won’t work.

If R\ge 2L then no matter what number X we take, either X\%L=X\%(2L) or X\%L+L=X\%(2L) meaning X\%L\le X\%2L which is not acceptable.