4383_Notes_3o3 - Math 4383 Section 3.3 Page 1 of 7 Number...

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Math 4383 Section 3.3 Page 1 of 7 Number Theory Chapter 3 Section 3.3 The Goldbach Conjecture This section picks up where the last left off and introduces us to several questions (some with answers, many still unknown) about the distribution of prime numbers. I will not expect you to remember all this material, but I may ask you to use the techniques we are learning to confirm or disprove a statement about primes. Twin Primes – How long can a consecutive string of composite numbers be?
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Math 4383 Section 3.3 Page 2 of 7 Gaps between primes Define the gap at prime p, denoted g(p) as the number of composite numbers between p and the next prime. Let’s find some values of this function Questions that mathematicians have asked – What values can g(p) have? What is the smallest prime p such that g(p) = a particular number Given a number in a certain range, how big can g(p) be? Is there any pattern in the values of g(p)?
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Math 4383 Section 3.3 Page 3 of 7 The Goldbach Conjecture Christian Goldbach, corresponding with Leonhard Euler, wondered if every even integer can be
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4383_Notes_3o3 - Math 4383 Section 3.3 Page 1 of 7 Number...

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