\beamer@endinputifotherversion {3.07pt} \headcommand {\slideentry {0}{0}{1}{1/1}{}{0}} \headcommand {\beamer@framepages {1}{1}} \headcommand {\sectionentry {1}{Math in the News}{2}{Math in the News}{0}} \headcommand {\beamer@sectionpages {1}{1}} \headcommand {\beamer@subsectionpages {1}{1}} \headcommand {\slideentry {1}{0}{2}{2/2}{}{0}} \headcommand {\beamer@framepages {2}{2}} \headcommand {\slideentry {1}{0}{3}{3/3}{}{0}} \headcommand {\beamer@framepages {3}{3}} \headcommand {\sectionentry {2}{Prime numbers}{4}{Prime numbers}{0}} \headcommand {\beamer@sectionpages {2}{3}} \headcommand {\beamer@subsectionpages {2}{3}} \headcommand {\beamer@subsectionentry {0}{2}{1}{4}{Definition and Examples}}\headcommand {\beamer@subsectionpages {4}{3}} \headcommand {\slideentry {2}{1}{1}{4/4}{Definition and Examples}{0}} \headcommand {\beamer@framepages {4}{4}} \headcommand {\slideentry {2}{1}{2}{5/6}{Definition and Examples}{0}} \headcommand {\beamer@framepages {5}{6}} \headcommand {\beamer@subsectionentry {0}{2}{2}{7}{Basic Results and Techniques}}\headcommand {\beamer@subsectionpages {4}{6}} \headcommand {\slideentry {2}{2}{1}{7/13}{Basic Results and Techniques}{0}} \headcommand {\beamer@framepages {7}{13}} \headcommand {\slideentry {2}{2}{2}{14/14}{Basic Results and Techniques}{0}} \headcommand {\beamer@framepages {14}{14}} \headcommand {\slideentry {2}{2}{3}{15/21}{Basic Results and Techniques}{0}} \headcommand {\beamer@framepages {15}{21}} \headcommand {\slideentry {2}{2}{4}{22/23}{Basic Results and Techniques}{0}} \headcommand {\beamer@framepages {22}{23}} \headcommand {\sectionentry {3}{How Many Primes?}{24}{How Many Primes?}{0}} \headcommand {\beamer@sectionpages {4}{23}} \headcommand {\beamer@subsectionpages {7}{23}} \headcommand {\beamer@subsectionentry {0}{3}{1}{24}{Euclid's Theorem}}\headcommand {\beamer@subsectionpages {24}{23}} \headcommand {\slideentry {3}{1}{1}{24/27}{Euclid's Theorem}{0}} \headcommand {\beamer@framepages {24}{27}} \headcommand {\slideentry {3}{1}{2}{28/30}{Euclid's Theorem}{0}} \headcommand {\beamer@framepages {28}{30}} \headcommand {\beamer@subsectionentry {0}{3}{2}{31}{The Prime Number Theorem}}\headcommand {\beamer@subsectionpages {24}{30}} \headcommand {\slideentry {3}{2}{1}{31/31}{The Prime Number Theorem}{0}} \headcommand {\beamer@framepages {31}{31}} \headcommand {\slideentry {3}{2}{2}{32/32}{The Prime Number Theorem}{0}} \headcommand {\beamer@framepages {32}{32}} \headcommand {\beamer@subsectionentry {0}{3}{3}{33}{Classical Conjectures and Recent Results}}\headcommand {\beamer@subsectionpages {31}{32}} \headcommand {\slideentry {3}{3}{1}{33/35}{Classical Conjectures and Recent Results}{0}} \headcommand {\beamer@framepages {33}{35}} \headcommand {\slideentry {3}{3}{2}{36/37}{Classical Conjectures and Recent Results}{0}} \headcommand {\beamer@framepages {36}{37}} \headcommand {\slideentry {3}{3}{3}{38/40}{Classical Conjectures and Recent Results}{0}} \headcommand {\beamer@framepages {38}{40}} \headcommand {\slideentry {3}{3}{4}{41/42}{Classical Conjectures and Recent Results}{0}} \headcommand {\beamer@framepages {41}{42}} \headcommand {\slideentry {3}{3}{5}{43/43}{Classical Conjectures and Recent Results}{0}} \headcommand {\beamer@framepages {43}{43}} \headcommand {\sectionentry {4}{Mersenne Primes}{44}{Mersenne Primes}{0}} \headcommand {\beamer@sectionpages {24}{43}} \headcommand {\beamer@subsectionpages {33}{43}} \headcommand {\beamer@subsectionentry {0}{4}{1}{44}{Definition and Examples}}\headcommand {\beamer@subsectionpages {44}{43}} \headcommand {\slideentry {4}{1}{1}{44/46}{Definition and Examples}{0}} \headcommand {\beamer@framepages {44}{46}} \headcommand {\beamer@subsectionentry {0}{4}{2}{47}{Mersenne's Claim}}\headcommand {\beamer@subsectionpages {44}{46}} \headcommand {\slideentry {4}{2}{1}{47/47}{Mersenne's Claim}{0}} \headcommand {\beamer@framepages {47}{47}} \headcommand {\slideentry {4}{2}{2}{48/49}{Mersenne's Claim}{0}} \headcommand {\beamer@framepages {48}{49}} \headcommand {\slideentry {4}{2}{3}{50/51}{Mersenne's Claim}{0}} \headcommand {\beamer@framepages {50}{51}} \headcommand {\slideentry {4}{2}{4}{52/53}{Mersenne's Claim}{0}} \headcommand {\beamer@framepages {52}{53}} \headcommand {\slideentry {4}{2}{5}{54/57}{Mersenne's Claim}{0}} \headcommand {\beamer@framepages {54}{57}} \headcommand {\sectionentry {5}{Perfect Numbers}{58}{Perfect Numbers}{0}} \headcommand {\beamer@sectionpages {44}{57}} \headcommand {\beamer@subsectionpages {47}{57}} \headcommand {\beamer@subsectionentry {0}{5}{1}{58}{Definition and Examples}}\headcommand {\beamer@subsectionpages {58}{57}} \headcommand {\slideentry {5}{1}{1}{58/59}{Definition and Examples}{0}} \headcommand {\beamer@framepages {58}{59}} \headcommand {\beamer@subsectionentry {0}{5}{2}{60}{Perfect Numbers and Mersenne Primes}}\headcommand {\beamer@subsectionpages {58}{59}} \headcommand {\slideentry {5}{2}{1}{60/63}{Perfect Numbers and Mersenne Primes}{0}} \headcommand {\beamer@framepages {60}{63}} \headcommand {\sectionentry {6}{Computing Mersenne Primes}{64}{Computing Mersenne Primes}{0}} \headcommand {\beamer@sectionpages {58}{63}} \headcommand {\beamer@subsectionpages {60}{63}} \headcommand {\beamer@subsectionentry {0}{6}{1}{64}{Known Mersenne Primes}}\headcommand {\beamer@subsectionpages {64}{63}} \headcommand {\slideentry {6}{1}{1}{64/64}{Known Mersenne Primes}{0}} \headcommand {\beamer@framepages {64}{64}} \headcommand {\slideentry {6}{1}{2}{65/65}{Known Mersenne Primes}{0}} \headcommand {\beamer@framepages {65}{65}} \headcommand {\beamer@subsectionentry {0}{6}{2}{66}{Lucas-Lehmer Test}}\headcommand {\beamer@subsectionpages {64}{65}} \headcommand {\slideentry {6}{2}{1}{66/66}{Lucas-Lehmer Test}{0}} \headcommand {\beamer@framepages {66}{66}} \headcommand {\slideentry {6}{2}{2}{67/67}{Lucas-Lehmer Test}{0}} \headcommand {\beamer@framepages {67}{67}} \headcommand {\slideentry {6}{2}{3}{68/68}{Lucas-Lehmer Test}{0}} \headcommand {\beamer@framepages {68}{68}} \headcommand {\beamer@subsectionentry {0}{6}{3}{69}{GIMPS}}\headcommand {\beamer@subsectionpages {66}{68}} \headcommand {\slideentry {6}{3}{1}{69/69}{GIMPS}{0}} \headcommand {\beamer@framepages {69}{69}} \headcommand {\beamer@subsectionentry {0}{6}{4}{70}{Conclusion}}\headcommand {\beamer@subsectionpages {69}{69}} \headcommand {\slideentry {6}{4}{1}{70/70}{Conclusion}{0}} \headcommand {\beamer@framepages {70}{70}} \headcommand {\partentry {Appendix}{1}} \headcommand {\beamer@partpages {1}{70}} \headcommand {\beamer@sectionpages {64}{70}} \headcommand {\beamer@subsectionpages {70}{70}} \headcommand {\beamer@appendixpages {71}} \headcommand {\slideentry {6}{0}{2}{71/71}{}{1}} \headcommand {\beamer@framepages {71}{71}} \headcommand {\slideentry {6}{0}{3}{72/72}{}{1}} \headcommand {\beamer@framepages {72}{72}} \headcommand {\beamer@partpages {71}{72}} \headcommand {\beamer@subsectionpages {71}{72}} \headcommand {\beamer@sectionpages {71}{72}} \headcommand {\beamer@documentpages {72}} \headcommand {\def \inserttotalframenumber {35}}