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 is an old version). In the forest each tree represents a lattice point on a coordinate plane. 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 when walking:

step 1: Start from The Great Tree (coordinates: 0, 0) and facing east

step 2: go towards the tree you are facing

step 3: if the number of trees you have walked to is a prime number, than turn clockwise 90 degrees

step 4: go to step 2

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


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