# A Parabola Sieve for Prime Numbers

A Parabola Sieve for Prime Numbers

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.

x=

2

y

N

(,-i)

2

i

P

,j

2

j

i

j

N

P

x

(ij,0)