Definition:Non-Pythagorean Prime

Definition

A non-Pythagorean prime is an odd prime number of the form:

$p = 4 n + 3$

where $n \in \Z_{\ge 0}$ is a positive integer.

Sequence

The sequence of non-Pythagorean primes begins:

$\begin{array} {r | r }

p & 4 n + 3 \\ \hline 3 & 4 \times 0 + 3 \\ 7 & 4 \times 1 + 3 \\ 11 & 4 \times 2 + 3 \\ 19 & 4 \times 4 + 3 \\ 23 & 4 \times 5 + 3 \\ 31 & 4 \times 7 + 3 \\ 43 & 4 \times 10 + 3 \\ 47 & 4 \times 17 + 3 \\ \end{array}$

Also see

• Fermat's Two Squares Theorem: such a prime number is never the sum of two squares

• Definition:Pythagorean Prime

Sources

There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page.