Mathematical Induction Method in Goldbach's Strong Conjecture


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Goldbach's strong conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states: ``Every even integer greater than 2 can be expressed as the sum of two primes". The conjecture has been shown to hold for all integers less than 4 ´┐Ż 10^18, but remains unproven despite considerable effort. As we know there are two conjectures, the weak and the strong conjecture. Many mathematicians have obtained important results about both conjectures. In this book we analyze if it could be appropriate to use Mathematical induction method to study Goldbach's strong conjecture. We use two properties that are satisfied for prime numbers, and based on these two properties, we show a way that, may be, it can be used to analyze and approach this conjecture by the Mathematical induction method.