\BOOKMARK [2][]{Outline0.1}{Math in the News}{} \BOOKMARK [2][]{Outline0.2}{Prime numbers}{} \BOOKMARK [3][]{Outline0.2.1.4}{Definition and Examples}{Outline0.2} \BOOKMARK [3][]{Outline0.2.2.7}{Basic Results and Techniques}{Outline0.2} \BOOKMARK [2][]{Outline0.3}{How Many Primes?}{} \BOOKMARK [3][]{Outline0.3.1.24}{Euclid's Theorem}{Outline0.3} \BOOKMARK [3][]{Outline0.3.2.31}{The Prime Number Theorem}{Outline0.3} \BOOKMARK [3][]{Outline0.3.3.33}{Classical Conjectures and Recent Results}{Outline0.3} \BOOKMARK [2][]{Outline0.4}{Mersenne Primes}{} \BOOKMARK [3][]{Outline0.4.1.44}{Definition and Examples}{Outline0.4} \BOOKMARK [3][]{Outline0.4.2.47}{Mersenne's Claim}{Outline0.4} \BOOKMARK [2][]{Outline0.5}{Perfect Numbers}{} \BOOKMARK [3][]{Outline0.5.1.58}{Definition and Examples}{Outline0.5} \BOOKMARK [3][]{Outline0.5.2.60}{Perfect Numbers and Mersenne Primes}{Outline0.5} \BOOKMARK [2][]{Outline0.6}{Computing Mersenne Primes}{} \BOOKMARK [3][]{Outline0.6.1.64}{Known Mersenne Primes}{Outline0.6} \BOOKMARK [3][]{Outline0.6.2.66}{Lucas-Lehmer Test}{Outline0.6} \BOOKMARK [3][]{Outline0.6.3.69}{GIMPS}{Outline0.6} \BOOKMARK [3][]{Outline0.6.4.70}{}{Outline0.6} \BOOKMARK [1][]{Outline1}{Appendix}{}