There are many properties of real numbers which hold a.e. with respect to Lebesgue measure, but are hard to check for specific numbers. A quick example.

Take a random number $x$ in $(0,1)$. Then for a given $p>1$ we may take its $p$-expansion $x=\sum_{i>0} a_{i,p}(x)p^{-i}$, $0\leq a_{i,p}(x)\leq p-1$. Digits $a_{i,p} (x)$ are independent and distributed uniformly on $\{0,1,\dots,p-1\}$. Hence by law of large numbers a.e. $x$ satisfy $$\lim_{N\rightarrow \infty} \frac1N \left|i\leq N: a_{i,p}(x)=c\right|=\frac 1p$$ for any given $c\in \{0,1,\dots,p-1\}$.

But there is no specific $x$ for which this is proved to hold simultaneosly for $p=2$ and $p=3$.