On Prime Distribution and Legendre's Conjecture
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The distribution of prime numbers is an important issue in number theory, and this study proposes an approach using color sequences. In this paper, we focus on the arrangement of prime numbers that appear when numbers 0, 1, 2,... are arranged in groups of 11, and analyze the regularity they exhibit, classifying them into four color sequences. Then, using these four color sequences, we discuss the Legendre's conjecture.
