A Parabola Sieve for Prime Numbers

x

9

The Russian mathematicians Yuri Matiyasevich and Boris Stechkin created this sieve for prime numbers. The parabola

x=

2

y

contains the subset

N

of points of the form

(

2

i

,-i)

and the subset

P

of points of the form



2

j

,j

, where

i

and

j

are integers greater than 1. Join all the points of

N

to all the points of

P

by lines; these lines cross the

x

axis at points with coordinates

(ij,0)

. All composite numbers are crossed by the lines, leaving the prime numbers.