Problems

Jack believes that he can place $99$ integers in a circle such that for each pair of neighbours the ratio between the larger and smaller number is a prime. Can he be right?

Katie and Charlotte had $4$ sheets of paper. They cut some of the sheets into $4$ pieces. They then cut some of the newly obtained papersheets also into $4$ pieces. They did this several more times, cutting a piece of paper into $4$. In the end they counted the number of sheets. Could this number be $2024$?