Diophantine Set

A set of positive integers is said to be Diophantine iff there exists a polynomial with integral coefficients in indeterminates such that

$S={Q(x_1,...,x_m)>=1:x_1>=1,...,x_m>=1}.$

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

See also

Prime Diophantine Equations

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References

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

Referenced on Wolfram|Alpha

Diophantine Set

Cite this as:

Weisstein, Eric W. "Diophantine Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DiophantineSet.html

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