Properties of Prime Numbers
We have seen two proofs in Chapter 2 showing the uniqueness of prime decompositions of integers (Theorem 1.8). The consequences of that theorem there and also in following chapters make it clear why Theorem 1.8 is called the fundamental theorem. The prime numbers mentioned in that theorem are distributed among the integers in a very peculiar way. One can get a feel for this by looking at the sequence of primes less than 150. We list these primes, writing the differences between consecutive primes below them, and writing those differences that are larger than all the previous differences in boldface.
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