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There is no obvious ordering for deciding which are the FIRST 15. You could order them by the sum of the three elements, or by the smallest, the largest or some other combination.

Excluding simple multiples of the basic triples, and ordered by the largest of the triple, they are

(3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29),

(12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), (16, 63, 65),

(33, 56, 65), (48, 55, 73), (13, 84, 85), (36, 77, 85), (39, 80, 89).

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Q: What is the first 15 pythagorean triples?
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