8581

This number is a prime.

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Prime 8581 is the hypotenuse length of a right triangle with legs 131 and 8580, where 131 is also prime. (Note that it is impossible for all three sides of an integer right triangle to be prime). The triangle (131, 8580, 8581) is the 11th largest right triangle having two prime sides; the smallest one is the classic (3,4,5). [Keith]