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Euclid

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... of the p[i]'s, so any of its prime divisors yields a new prime number (Euclid only considered the case n=3). || infinitely many primes. Analytic number theory has given a further refinement of Euclid's theorem by determining a | || this product of primes. This theorem was known to the Greek mathematician Euclid, who proved that there are | * Euclid: Assume there are a finite number of primes p[1],...,p[n], then p[1] p[2] ... p[n]+1 is not divisible by any generalisation. For example, Euclid's proof easily shows that there are an infinite number of primes of ...



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Sources list for EUCLID:

Moore, R. (1993). Hobnobbing with Euclid. The Midwest Quarterly, 35(1), 21.
Concepts of Beauty

 

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