\contentsline {section}{\numberline {1}Introduction}{1}
\contentsline {section}{\numberline {2}Geometric Arguments: $p=19,23,29,31,...$}{2}
\contentsline {section}{\numberline {3}The Quartic Criterion}{2}
\contentsline {subsection}{\numberline {3.1}$p=29$}{3}
\contentsline {subsection}{\numberline {3.2}$p=31$}{4}
\contentsline {subsection}{\numberline {3.3}$p=37$}{4}
\contentsline {subsection}{\numberline {3.4}$p=41$}{4}
\contentsline {subsection}{\numberline {3.5}$p=43$}{5}
\contentsline {subsection}{\numberline {3.6}$p=47$}{5}
\contentsline {subsection}{\numberline {3.7}$p=53$}{5}
\contentsline {subsection}{\numberline {3.8}$p=59$}{6}
\contentsline {subsection}{\numberline {3.9}$p=61$}{6}
\contentsline {subsection}{\numberline {3.10}$p=67$}{6}
\contentsline {subsection}{\numberline {3.11}$p=71$}{7}
\contentsline {subsection}{\numberline {3.12}$p=73$}{7}
\contentsline {subsection}{\numberline {3.13}$p=79$}{7}
\contentsline {subsection}{\numberline {3.14}$p=83$}{8}
\contentsline {subsection}{\numberline {3.15}$p=89$}{8}
\contentsline {subsection}{\numberline {3.16}$p=97$}{9}
\contentsline {section}{\numberline {4}Appendix: The Code}{9}