The Nature of Mathematics, 12th Edition
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Chapter1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
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Links

Videos:

Sieve of Eratosthenes  (time: 2:55)
http://www.youtube.com/watch?v=9m2cdWorIq8

Prime Numbers (time: 1:42)
http://www.youtube.com/watch?v=2gG8kFFkTLY

Largest Prime (time: 1:14)
http://www.youtube.com/watch?v=Memk877qX8A

History

This is one of the best all around sites that I have found. It is titled "The MacTutor History of Mathematics Archive."
http://www-history.mcs.st-and.ac.uk/~history/

This is an award-winning site that links to all sorts of mathematics information.
http://archives.math.utk.edu/

Fermat:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Fermat.html

Hilbert:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Hilbert.html

Mersenne:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Mersenne.html

Wallis:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Wallis.html

Reference Topics

This is a very useful site. You enter any positive integer and it will return a prime factorization of that integer.
http://www.rsok.com/~jrm/factor.html

The Prime Pages; there is a lot here. Articles include the "Guinness book of" prime number records, how to find primes, conjectures and open problems, and some special types of primes:
http://www.utm.edu/research/primes/

This is a nice site, but is probably more than you want to know about primes:
http://mathforum.org/library/topics/prime_numbers/

Listen to the primes:
http://www.utm.edu/research/primes/programs/music/listen/

View the primes:
http://www.lactamme.polytechnique.fr/Mosaic/images/CONFORME.31.Fi.D/display.html

The largest known primes:
http://www.utm.edu/research/primes/largest.html

A nice reference for perfect numbers is at this site:
http://www-history.mcs.st-and.ac.uk/history/HistTopics/Perfect_numbers.html

There is a lot of interesting material on the web concerning Goldbach's conjecture. The follow site provides a numerical calculator.
http://pass.maths.org.uk/issue2/xfile/

This is a fun site that combines the ideas of divisibility and patterns on Pascal's Triangle (which was introduced in Chapter 1).
http://nlvm.usu.edu/en/nav/frames_asid_181_g_4_t_1.html