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GaussInt

 GIsieve
 Gaussian prime generator

 Calling Sequence GIsieve(m)

Parameters

 m - positive integer

Description

 • The GIsieve function generates a list of Gaussian primes $x+Iy$ whose norms are less than or equal to ${m}^{2}$, and who are located in the one-eighth plane defined by $0\le y .
 • Any prime found in that area has seven more associated primes: $-x+Iy$, $±x-Iy$,  $±y-Ix$, except for $1+I$ which exceptionally lies on $x=y$ and has only three associated primes.

Examples

 > $\mathrm{with}\left(\mathrm{GaussInt}\right):$
 > $\mathrm{GIsieve}\left(10\right)$
 $\left[{14}{,}\left[{1}{+}{I}{,}{1}{+}{2}{}{I}{,}{3}{,}{2}{+}{3}{}{I}{,}{1}{+}{4}{}{I}{,}{2}{+}{5}{}{I}{,}{1}{+}{6}{}{I}{,}{4}{+}{5}{}{I}{,}{7}{,}{2}{+}{7}{}{I}{,}{5}{+}{6}{}{I}{,}{3}{+}{8}{}{I}{,}{5}{+}{8}{}{I}{,}{4}{+}{9}{}{I}\right]\right]$ (1)