\beamer@endinputifotherversion {3.10pt} \beamer@sectionintoc {1}{Math in the News}{2}{0}{1} \beamer@sectionintoc {2}{Prime numbers}{4}{0}{2} \beamer@subsectionintoc {2}{1}{Definition and Examples}{4}{0}{2} \beamer@subsectionintoc {2}{2}{Basic Results and Techniques}{7}{0}{2} \beamer@sectionintoc {3}{How Many Primes?}{24}{0}{3} \beamer@subsectionintoc {3}{1}{Euclid's Theorem}{24}{0}{3} \beamer@subsectionintoc {3}{2}{The Prime Number Theorem}{31}{0}{3} \beamer@subsectionintoc {3}{3}{Classical Conjectures and Recent Results}{33}{0}{3} \beamer@sectionintoc {4}{Mersenne Primes}{44}{0}{4} \beamer@subsectionintoc {4}{1}{Definition and Examples}{44}{0}{4} \beamer@subsectionintoc {4}{2}{Mersenne's Claim}{47}{0}{4} \beamer@sectionintoc {5}{Perfect Numbers}{58}{0}{5} \beamer@subsectionintoc {5}{1}{Definition and Examples}{58}{0}{5} \beamer@subsectionintoc {5}{2}{Perfect Numbers and Mersenne Primes}{60}{0}{5} \beamer@sectionintoc {6}{Computing Mersenne Primes}{64}{0}{6} \beamer@subsectionintoc {6}{1}{Known Mersenne Primes}{64}{0}{6} \beamer@subsectionintoc {6}{2}{Lucas-Lehmer Test}{66}{0}{6} \beamer@subsectionintoc {6}{3}{GIMPS}{69}{0}{6}