Authors: Chongxi Yu
Prime numbers are the basic numbers and are crucially important. There are many conjectures concerning primes that have been challenging mathematicians for hundreds of years. Goldbach's conjecture is one of the oldest and most well-known unsolved problems in number theory and in all of mathematics. A kaleidoscope can produce an endless variety of colorful patterns and it looks like magic, but when you open one and examine it, it contains only very simple, loose, colored objects such as beads or pebbles and bits of glass. Humans are very easily cheated by 2 words, infinite and anything, because we never see infinite and anything, and so we always make a simple thing complex. Goldbach’s conjecture is about all very simple numbers, with the pattern of prime numbers similar to a “kaleidoscope” of numbers. If we divided all even numbers into 5 groups and primes into 4 groups, Goldbach’s conjecture becomes much simpler. Here we give a clear proof for Goldbach's conjecture based on the fundamental theorem of arithmetic, the prime number theorem, and Euclid's proof that the set of prime numbers is endless.
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