Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

In the math.se question Proof of no prime-representing polynomial in 2 variables, Alon Amit asks if Ribenboim's claim that a prime-representing polynomial (a Diophantine polynomial in which the positive values are precisely the primes) must have at least three variables has been proven. Alon suggested that perhaps the number was a typo, that all that is known is that (trivially) no univariate polynomial is prime-representing.

As of Jones 1982 [1, p. 550] the question of the existence of a universal Diophantine equation in two variables was open, so certainly it was not known that the number of variables for the special case of the primes was more than 2 at that time.

[1] James P. Jones, "Universal Diophantine equation", The Journal of Symbolic Logic 47:3 (1982), pp. 549-571.

share|improve this question

1 Answer 1

Davis [1] writes that the two-variable case of universal Diophantine equations is still open as of 2006. (Ribenboim's book was published in 1996.) So the question of a prime-representing polynomial in two variables was (and, presumably, is) still open.

[1] Martin Davis, [FOM] Decidability of Diophantine equations, post to the FOM mailing list, December 14 2006.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.