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
Has Statement Form
In Branch
Source Furstenberg's proof of the infinitude of primes - Wikipedia
Principal Result Of
Source Hillel Furstenberg (Wikipedia)
Proved By
Source Furstenberg's proof of the infinitude of primes - Wikipedia
Sources
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.
Proved By: Hillel Furstenberg, Lead sentence
In mathematics, particularly in number theory, Hillel Furstenberg's proof of the infinitude of primes is a topological proof that the integers contain infinitely many prime numbers.
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
View the SourceHillel Furstenberg (Wikipedia)
Principal Result Of: Hillel Furstenberg, Body, workQuote, Principal Result Of: Hillel Furstenberg, Body, work
producing an innovative topological proof of the infinitude of prime numbers in 1955
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.