Prime plus two positive squares

Prove that every integer n greater than 14 can be represented as n=p+x^2+y^2, where p is an odd prime and x and y are positive integers.

Background

This is the principal square-representation conjecture studied in the paper. The authors computationally prove it for 14<n<1026, but the unrestricted assertion remains conjectural.

References

If $n>14$, then $n=p+x2+y2$, where $p$ is an odd prime and $x, y$ are positive integers.

— Computational results on sums of a prime with squares or cubes  (2609.20505 - Applegate et al., 17 Sep 2026) in Conjecture 1.1, Section 1