Teaser 2836: Squaring up

From The Sunday Times, 29th January 2017 [link]

Alice had a large collection of one centimetre square tiles. She used them to make a set of some larger squares of different sizes, all with sides of less than a metre. When I saw these squares I removed one corner tile from each. Then, for each mutilated shape, Alice moved the minimum number of tiles to transform it into a rectangle. Overall she moved two hundred tiles. This resulted in a set of rectangles all of whose sides were a prime number of centimetres long.

What (in increasing order) were the lengths of the sides of her original squares?

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