How can I prove that there doesnt exist a triangle whose sides are prime numbers?

Answer 1

You mean RIGHT triangle, correct? Obviously, 3,5, and 7 makes a triangle.

The easiest way, I think, is to note that you can't have a right triangle with 3 odd numbers, since the sum of the squares of two odd numbers is an even number. That means one of the sides has to be 2 (the only even prime number), but there are no Pythagorean triples with the number 2.

Answer 2

If you are looking for a right triangle, then a^2 + b^2 = c^2

Since all prime numbers except 2 are odd, then either a or b would have to be two, and 2^2 is 4. There would have to exist two perfect (odd) squares exactly 4 apart. There are not any, as the minimum distance between two odd squares is 8. (1 and 3)

Answer 3

There do exist triangles whose sides are prime numbers.
sides of 3, 5, 7
sides of 5, 7, 11
sides of 7, 11, 13
sides of 5, 11, 13
etc.

Answer 4

3, 5, 7 can form a triangle. Therefore, there exists such a triangle whose sides are prime numbers.

I guess the original problem should be a right triangle.

If three prime numbers can form a right triangle, we have
l^2+m^2 = n^2, l l^2 = (n+m)(n-m)
Therefore l cannot be a prime.

Answer 5

Where did you ever get -that- silly notion? Given 3 lengths, you can -always- form a triangle with them.

Doug