Is the primality problem with unary input NLOGSPACE-Hard?
This language is in $\mathsf{LOGSPACE}$ via trial division. It is also known logarithmic space is neccessary ([1]). For a generalization to sparse sets, see bounded language complete for NSPACE(log n)?. For hardness in binary case, see Are the problems PRIMES, FACTORING known to be P-hard?.

[1] J. Hartmanis, L. Berman, On tape bounds for single letter alphabet language processing. Theoretical Computer Science vol. 3 http://www.sciencedirect.com/science/article/pii/0304397576900244