Diophantine Set

A set $S$ of Positive integers is said to be Diophantine Iff there exists a Polynomial $Q$ with integral coefficients in $m\geq 1$ indeterminates such that

$$S=\{Q(x_1,\ldots,x_m)\geq 1 : x_1\geq 1, \ldots, x_m\geq 1\}.$$

It has been proved that the set of Prime numbers is a Diophantine set.

References

Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 189-192, 1995.