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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Since there are an infinite amount of whole numbers to make Pythagorean triples, there would be an infinite amount of Pythagorean triples to make.
No.
3 4 5 6 8 10 9 40 41 20 21 29 9 12 15 ...and factors of those such as the first 2 examples.
( 3 , 4 , 5 ) ( 5, 12, 13) ( 7, 24, 25)
You seem to have squashed the numbers together but 4, 3 and 5 make up a Pythagorean triple.