# Is any ec-number larger than $73$ the sum of a square and a cube?

An ec-number concatenates the Mersenne numbers $$2^n-1$$ and $$2^{n-1}-1$$ decimal (see also here A conjecture about numbers of the form $$10^{m}(2^{k}−1)+2^{k-1}−1$$, where $$m$$ is the number of decimal digits of $$2^{k-1}$$. for further details)

Besides $$31$$ and $$73$$ , are there ec-primes $$p$$ (or at least ec-numbers) that can be written in the form $$p=a^3+b^2$$ with positive integers $$a$$ and $$b$$ ? I checked the ec-primes with MAGMA, but $$ec(46)$$ is still an unsolved case.