It's very unlikely that they are related. 1/e which is approximately 0.37 is the solution to the problem you're referring to but the occurrence of 37 depends on the choice of base. It just happens to be the case that in base 10 we find that round(1/e*10^2)=37 but it would be different in other bases.

Meanwhile, the median value for the second prime is completely independent of the choice of base.