Examples of Primes in Quadratic Integers

definitionquadratic-integers

Primes in Quadratic Integers differ from primes in $\mathbb{Z}$.

In $\mathbb{Z}[i]$

Primes in $\mathbb{Z}[i]$ are numbers with prime norm or equal to primes in $\mathbb{Z}$.

Some primes in $\mathbb{Z}[i]$ with small norm

• $1+i,1-i$ have norm $2$.
• $1+2i,1-2i$ have norm $5$.
• $2+3i,2-3i$ have norm 13.
• $3$
• $7$
• $11$