Why is the study of prime numbers fundamental to number theory?
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Prime numbers are the building blocks of integers, as every integer greater than one can be expressed as a product of primes. This unique factorization property makes primes essential in number theory, influencing concepts such as divisibility, congruences, and the distribution of numbers. Their properties also lead to important results and conjectures, such as the Fundamental Theorem of Arithmetic and the Goldbach Conjecture.