If 500 people pull on a rope with 25 pounds of force each, the tension is 6,250 pounds, not 13,000. Your math would be correct if one end of the rope were anchored.
(Or put another way: if two people pull on a rope with 50 pounds of force, the tension is 50 pounds, not 100.)
(Or put another way: if two people pull on a rope with 50 pounds of force, the tension is 50 pounds, not 100.)