In the 1986 book *[An Introduction to the Theory of Surreal Numbers]( https://doi.org/10.1017/CBO9780511629143)*, Gonshor, on page 117, notes that it is an open problem whether $\omega(\sqrt{2}+1)+1$ is a prime, using the standard definition of integral number he introduces earlier in the chapter.

Is this still an open problem? The book is a couple decades old (picked it up at the library), and searching for surreal numbers doesn't turn up many results.

Thanks