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.


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