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A new proof of Euclid’s theorem. (English) Zbl 1228.11011

The author provides a new proof of Euclid’s theorem that the number of primes is infinite, as the result of a process that may be continued indefinitely: Let \(N_1>1\). Then \(N_1\) and \(N_1+1\) are coprime because they are consecutive integers, so \(N_2=N_1(N_1+1)\) has at least two distinct prime factors. Then as before, \(N_2\) and \(N_2+1\) are consecutive integers, so \(N_3=N_2(N_2+1)\) must have at least three distinct prime factors, and so on.

MSC:

11A41 Primes
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