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This paper presents a logical explanation for the Twin Prime and Goldbach Conjectures using base-10 reasoning. By observing that all prime numbers in base 10 end with 1, 3, 7, or 9 (excluding 5 as a special case), the study explores how the consistent +2 differences among these unit digits naturally support the occurrence of twin primes. It further shows that these same digit patterns account for all even numbers, providing a simple and intuitive foundation for Goldbach’s claim that every even number is the sum of two primes. This approach demonstrates how the universal structure of base 10 arithmetic explains these long-standing mysteries through pure logic rather than complex computation.