Parabola has an easily verifiable property.
The equation of the segment is , from which .
This may be a curious fact in its own right. What does it say? Taken at a face value, it simply shows a way to obtain the product of two numbers in the presence of a graph of parabola. But Yu. B. Matiyasevich and B. S. Stechkin have recognized that, if we restrict the consideration to the integers, the number so obtained will be composite (excluding of course the case where one of or equals 1.) It follows that by joining all points and , where , the only integer points on -axis that won't be crossed correspond to prime numbers . (See also Etudes, and Catching Primes.)
A parabolic sieve of prime numbers - who would have thought!?