Originally Posted by

**Bernhard** "It is not true in general that an irreducible element is necessarily prime."

They give as an example the element 3 in the quadratic integer ring $\displaystyle R =\mathbb{Z} [\surd -5 ] $

They assert that the element** 3 is irreducible but not prime**.

I am struggling to show rigorously that 3 is irreducible in R, despite D&F's reference to the calculations on page 273 (see attached)

Can someone please help me produce a formal and rigorous demonstration that 3 is irreducible.