Analyzing The Goldbach Conjecture

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Analyzing the Goldbach Conjecture
Introduction
Proposed in 1742 by Christian Goldbach, the Goldbach Conjectures have remained among the most famous mathematical problems ever proposed. The conjectures were first identified in a letter by him written to fellow famous mathematician, Leonhard Euler, the founder of Euler’s constant (2.718). The conjectures basically state that every even integer greater than two is a sum of two primes, and every odd integer greater than five is a sum of three primes. Though there is still a lot to discover about the conjectures, mathematicians generally view them as true. In this mathematical exploration I shall discuss in detail both of Goldbach’s conjectures and the mathematical procedures that occur.
Rationale
The reason I chose to research this topic is because a while back I had realized that every even number other than two could be reached by adding two prime numbers. I was in Algebra class and I was adding numbers together and I noticed a pattern emerging that the even numbers were always the sum of two odd numbers. Moreover when adding more numbers together I realized it was actually the sum of two prime numbers. My Algebra teacher told me she never noticed this pattern and this fascinated me as I thought had found something that no one had ever found before. When researching possible Calculus Exploration IA topics I came upon this topic again. That is why I chose to do this project.

Aim of Exploration
For over 270 years, mathematicians have been analyzing the Goldbach Conjecture. In all this time no one has been able to completely prove the strong conjecture. The weak conjecture was proved using the Riemann hypothesis. The aim of this exploration is to determine the validity of this co...

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...in no time they will find a formula that will be able to prove the whole theorem..
Reflection
Overall, I enjoyed researching this topic and learned a lot from it. When i first saw this topic, I assumed that there was nothing to it and it was quite simple. However, when I started researching the topic I found out how mistaken I was. The accumulation of evidence leading to the proof of the Weak Conjecture and the information on the Strong Conjecture was substantial. It was quite interesting seeing how a theorem, that at first glance seemed so simple was actually quite complicated. It took over 270 years just to solve the weak conjecture! My view of mathematics and calculus has changed as I now see that what we are doing currently is nothing compared to the difficulty of these equations. It was an enjoyable experience and I would not mind writing another exploration.

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