Ant Betty

Level pending

Ant Betty is lost in a forest and she is asking us to help her (she has called us with her smart phone, however she doesn't have GPS because it is an old version). The forest is a coordinate plane and there is a tree on every lattice point. Ant Betty doesn't know where she is, but she can tell us how has she walked, where she started and how many tree she has passed in her journey. She followed these rules of conduct dictated by the ministry of Antlandia:

When going to the forest one must ALWAYS start walking form the Great Tree (coordinates: 0, 0) and facing east.

step 1. The person walks towards the tree he/she is facing;

step 2: if the number of trees the person has walked to is a prime number, than he/she must turn clockwise 90 degrees;

step 4: repeat from step 1 until the person doesn't reach its location.

Ant Betty passed 7466006 trees (not counting the Great Tree, but counting the current tree). Let (x, y) be the coordinates of the tree at which Ant Betty is now. Help Ant Betty by telling her x+y.


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