Equal prime block language is not context-free

The language $\{0^p{1}^p:p\text{ is prime}\}$ is not context-free. For a proposed pumping length, start with a larger prime $p$. Pumping unequal numbers of zeros and ones breaks equality; if the positive changes are equal to $d$, pumping with exponent $p+1$ gives the composite common block length $p(1+d)$.