A Short Introduction to the Prime Number Theorem
نویسنده
چکیده
We briefly discuss the history of the prime number theorem and summarize Newman’s 1980 proof using complex analysis. I have attempted to convey the flavor of the proof without deviating too much from heuristic arguments; all details are left as exercises to the reader. “There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout. The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision.” D. Zagier
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