Hillel Furstenberg's proof of the infinitude of primes is a topological argument, published in 1955 in the American Mathematical Monthly, showing that there are infinitely many prime numbers. Furstenberg wrote the proof as an undergraduate at Yeshiva University. Unlike Euclid's classical argument, Furstenberg's proof proceeds by contradiction, and although it is framed in terms of a topology on the integers, its real content concerns properties of arithmetic sequences.
Facts
StatementDefine a topology on the integers Z by declaring a subset U ⊆ Z to be an open set if and only if it is a union of arithmetic sequences S(a, b) for a ≠ 0, or is empty 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Source Furstenberg's proof of the infinitude of primes - Wikipedia
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1. Furstenberg's proof of the infinitude of primes - Wikipedia
Furstenberg's proof section
Define a topology on the integers Z by declaring a subset U ⊆ Z to be an open set if and only if it is a union of arithmetic sequences S(a, b) for a ≠ 0, or is empty
Lead section
The proof was published in 1955 in the American Mathematical Monthly while he was still an undergraduate student at Yeshiva University.
In Branch: Number Theory, Lead sentence
In mathematics, particularly in number theory, Hillel Furstenberg's proof of the infinitude of primes is a topological proof that
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