We note that this is a difference of squares, so $513^2 - 487^2 = (513+487)(513-487) = (1000)(26) = \boxed{26000}$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the value of $513^2 - 487^2$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
26000
What is the value of $513^2 - 487^2$?
test