Using the same thing.........a triangle whose sides are 4 and the square root of 3 i........16 - 3 = 13......the square root of 13........13 is prime.....
In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, 1 : 1 + 5 2 {\displaystyle 1:{\tfrac {1+{\sqrt {5}}}{2}}} , which is 1 : φ {\displaystyle 1:\varphi } (the Greek letter phi), where is approximately 1.618.
https://en.wikipedia.org/wiki/Golden_rectangle
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