# A (rewritten!) Prime Product

Calculus Level pending

Suraj is interested in how the dimensions of a rectangle affect its area. He sets up a ratio of the area of a square to the area of a rectangle of equal perimeter ($$\dfrac { { A }_{ square} }{ { A }_{ rectangle } }$$).The sides of the rectangle are modeled by $$s-a$$ and $$s+a$$, while the side length of the square is $$s$$. Suraj's friend tells him that the product of all of his ratios in which $$s$$ is a prime number greater than two and $$a=1$$ can be determined. He stated that the product would be equal to the area of a particular circle multiplied by $$\pi$$. If the radius of the circle is $$r$$, then what is the value of $$\left\lceil 1000r \right\rceil$$?

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