A Parabola Sieve for Prime Numbers

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The Russian mathematicians Yuri Matiyasevich and Boris Stechkin created this sieve for prime numbers. The parabola contains the subset of points of the form and the subset of points of the form , where and are integers greater than 1. Join all the points of to all the points of by lines; these lines cross the axis at points with coordinates . All composite numbers are crossed by the lines, leaving the prime numbers.

Contributed by: Enrique Zeleny (February 2013)
Open content licensed under CC BY-NC-SA


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References

[1] Gaussianos. "La sorprendente criba de la parábola." (in Spanish) (Jan 31, 2013) gaussianos.com/la-sorprendente-criba-de-la-parabola/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+gaussianos+%28Gaussianos%29.

[2] Y. Matiyasevich and B. Stechkin. "A Visual Sieve for Prime Numbers." (Jan 31, 2013) logic.pdmi.ras.ru/~yumat/personaljournal/sieve/sieve.html.



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